Daily Papers

Anterior-posterior polarization in the Drosophila oocyte requires posterior localization of oskar mRNA. oskar mRNA is produced in the anteriorly situated nurse cells, moved into the oocyte, and assembled into oskar-Staufen ribonucleoprotein particles (RNPs). These RNPs then move through the oocyte and interact with the cortex, where myosin-V binds them to the actin network and kinesin-1 removes them along cortically anchored microtubules. This cortical tug-of-war takes place against an anterior-to-posterior decrease in microtubule density. How the interplay between cytoplasmic transport and cortical binding and unbinding produces a stable posterior cap is unclear. Here, we combine quantitative microscopy, photoconversion experiments, experimental perturbations, and biophysical modeling to show that posterior localization emerges from position-dependent cortical exchange coupled to cytoplasmic diffusion. Our model, which accounts for the tendency of RNPs to demix, suggests that two key parameters that determine the observed localization pattern are the total amount of oskar and the ratio of cortical unbinding to binding rates (the exchange equilibrium constant). Given oskar volume fractions in wild-type, the measured exchange constant is such that oskar localizes to the posterior cortex without demixing. If the balance is broken, say by increasing unbinding rates, oskar irreversibly demixes into cytoplasmic droplets. This is consistent with observations from our experimental perturbations. Our results show how bulk diffusion and cortical exchange, in the face of oskar RNPs' self-attraction, convert a cytoskeletal asymmetry into robust developmental polarity.

The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have ignited investigation into important aspects of molecular diffusion in 3D cellular architectures. This paper describes fundamental mechanics of diffusion with equations for modeling these dynamic processes under a variety of scenarios in 3D cellular tissue constructs. The effects of these diffusion processes and resultant concentration gradients are described in the context of the major molecular signaling pathways in stem cells that both mediate and are influenced by gas and nutrient concentrations, including how diffusion phenomena can affect stem cell state, cell differentiation, and metabolic states of the cell. The application of these diffusion models and pathways is of vital importance for future studies of developmental processes, disease modeling, and tissue regeneration.

The mobility of particles in fluid membranes is a fundamental aspect of many biological processes. In a 1975 paper [1], Saffman and Delbr\"uck demonstrated how the presence of external Stokesian solvents is crucial in regularising the apparently singular flow within an infinite flat membrane. In the present paper, we extend this classical work and compute the rotational mobility of a rigid finite-sized particle located inside a spherical membrane embedded in Stokesian solvents. Treating the particle as a spherical cap, we solve for the flow semi-analytically as a function of the Saffman-Delbr\"uck (SD) length (ratio of membrane to solvent viscosity) and the solid angle formed by the particle. We study the dependence of the mobility and flow on inclusion size and SD length, recovering the flat-space mobility as a special case. Our results will be applicable to a range of biological problems including rotational Brownian motion, the dynamics of lipid rafts, and the motion of aquaporin channels in response to water flow. Our method will provide a novel way of measuring a membrane's viscosity from the rotational diffusion of large inclusions, for which the commonly used planar Saffman-Delbr\"uck theory does not apply.

Computational pathology has made significant progress in recent years, fueling advances in both fundamental disease understanding and clinically ready tools. This evolution is driven by the availability of large amounts of digitized slides and specialized deep learning methods and models. Multiple self-supervised foundation feature extractors have been developed, enabling downstream predictive applications from cell segmentation to tumor sub-typing and survival analysis. In contrast, generative foundation models designed specifically for histopathology remain scarce. Such models could address tasks that are beyond the capabilities of feature extractors, such as virtual staining. In this paper, we introduce CytoSyn, a state-of-the-art foundation latent diffusion model that enables the guided generation of highly realistic and diverse histopathology H&E-stained images, as shown in an extensive benchmark. We explored methodological improvements, training set scaling, sampling strategies and slide-level overfitting, culminating in the improved CytoSyn-v2, and compared our work to PixCell, a state-of-the-art model, in an in-depth manner. This comparison highlighted the strong sensitivity of both diffusion models and performance metrics to preprocessing-specific details such as JPEG compression. Our model has been trained on a dataset obtained from more than 10,000 TCGA diagnostic whole-slide images of 32 different cancer types. Despite being trained only on oncology slides, it maintains state-of-the-art performance generating inflammatory bowel disease images. To support the research community, we publicly release CytoSyn's weights, its training and validation datasets, and a sample of synthetic images in this repository: https://huggingface.co/Owkin-Bioptimus/CytoSyn.

Identifying subtle phenotypic variations in cellular images is critical for advancing biological research and accelerating drug discovery. These variations are often masked by the inherent cellular heterogeneity, making it challenging to distinguish differences between experimental conditions. Recent advancements in deep generative models have demonstrated significant potential for revealing these nuanced phenotypes through image translation, opening new frontiers in cellular and molecular biology as well as the identification of novel biomarkers. Among these generative models, diffusion models stand out for their ability to produce high-quality, realistic images. However, training diffusion models typically requires large datasets and substantial computational resources, both of which can be limited in biological research. In this work, we propose a novel approach that leverages pre-trained latent diffusion models to uncover subtle phenotypic changes. We validate our approach qualitatively and quantitatively on several small datasets of microscopy images. Our findings reveal that our approach enables effective detection of phenotypic variations, capturing both visually apparent and imperceptible differences. Ultimately, our results highlight the promising potential of this approach for phenotype detection, especially in contexts constrained by limited data and computational capacity.

The cell cortex and cell adhesion contribute to the mechanics of epithelial cells and hence tissues. Vertex models of epithelia represent the cell cortex and cell adhesion, but these models mostly ignore the other subcellular structures that compose the cytoplasm surrounded by the cortex. Here, we reveal the mechanical consequences of these structures in a minimal vertex model of an epithelial monolayer, in which the single-cell energy includes a cytoplasmic contribution that represents, e.g., the cost of confinement of cytosolic polymers. Strikingly, our simulations show that the buckling transition of the monolayer under compression becomes discontinuous in an intermediate range of values of the associated cytoplasmic modulus. By asymptotic solution of this buckling problem in the continuum limit of the model, we explain this reentrant behaviour in terms of the tricritical points of a sixth-order Landau theory. Our results thus underline how cell-scale mechanics beyond the cortex and cell adhesion can change emergent, tissue-scale behaviour even qualitatively.

Cell painting is a popular technique for creating human-interpretable, high-contrast images of cell morphology. There are two major issues with cell paint: (1) it is labor-intensive and (2) it requires chemical fixation, making the study of cell dynamics impossible. We train a diffusion model (Morphological Observation Neural Enhancement Tool, or MONET) on a large dataset to predict cell paint channels from brightfield images. We show that model quality improves with scale. The model uses a consistency architecture to generate time-lapse videos, despite the impossibility of obtaining cell paint video training data. In addition, we show that this architecture enables a form of in-context learning, allowing the model to partially transfer to out-of-distribution cell lines and imaging protocols. Virtual cell painting is not intended to replace physical cell painting completely, but to act as a complementary tool enabling novel workflows in biological research.

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments that have a permeable boundary. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. In the limit of large bulk diffusivity an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation.

Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.

Traditional theories of electrolyte and polyelectrolyte solutions overlook ion and polymer hydration, yielding an overly idealized perspective of the thermodynamic and dynamic properties of these solutions. In particular, the propensity of certain ions to increase or decrease the water diffusion coefficient at low solution concentrations, is poorly understood, a phenomenon that correlates strongly with the Hofmeister series describing the influence of salts on the solubility and self-assembly of synthetic and biomacromolecules as well as colloidal particles. These ion-specific effects have profound ramifications in diverse biological, medical science and technological applications. We address the general problem of understanding ion and uncharged water-soluble polymer hydration through molecular dynamics (MD) simulations of representative water-soluble polymers, polyacrylamide (PAM) and polyethylene oxide (PEO), in aqueous salt solutions. Careful attention is given to the capacity of our model to reproduce observed trends of added monovalent salts on the diffusion coefficient of water. Reproducing these ion-specific trends in the mobility of water has been a recurrent challenge in prior MD simulations of aqueous solutions based on a physically realistic model of water. Our work on salt solutions represents an important advance on which we build our modeling of aqueous polymer solutions with added salts. Simulations of our model polymers reveal an extended nanoscale dynamic hydration layer having a scale on the order of one nanometer (nm) in which the mobility is perturbed from its bulk value, and the mobility gradient in this layer appears to obey a near universal functional form.

Hematoxylin and Eosin (H&E) staining is widely regarded as the standard in pathology for diagnosing diseases and tracking tumor recurrence. While H&E staining shows tissue structures, it lacks the ability to reveal specific proteins that are associated with disease severity and treatment response. Immunohistochemical (IHC) stains use antibodies to highlight the expression of these proteins on their respective cell types, improving diagnostic accuracy, and assisting with drug selection for treatment. Despite their value, IHC stains require additional time and resources, limiting their utilization in some clinical settings. Recent advances in deep learning have positioned Image-to-Image (I2I) translation as a computational, cost-effective alternative for IHC. I2I generates high fidelity stain transformations digitally, potentially replacing manual staining in IHC. Diffusion models, the current state of the art in image generation and conditional tasks, are particularly well suited for virtual IHC due to their ability to produce high quality images and resilience to mode collapse. However, these models require extensive and diverse datasets (often millions of samples) to achieve a robust performance, a challenge in virtual staining applications where only thousands of samples are typically available. Inspired by the success of multitask deep learning models in scenarios with limited data, we introduce STAINDIFFUSER, a novel multitask diffusion architecture tailored to virtual staining that achieves convergence with smaller datasets. STAINDIFFUSER simultaneously trains two diffusion processes: (a) generating cell specific IHC stains from H&E images and (b) performing H&E based cell segmentation, utilizing coarse segmentation labels exclusively during training. STAINDIFFUSER generates high-quality virtual stains for two markers, outperforming over twenty I2I baselines.

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.

Destructive single-cell measurements provide unpaired population snapshots rather than observations of the same cells across conditions. Local cell states and transition requests may also be insufficient to distinguish responses across source populations. We introduce TempoBridge, a common source-conditioned transport formulation for temporal, genetic, and chemical population transitions. Source cells initialize latent transport and provide a fixed empirical population summary. The velocity field receives this summary alongside the evolving cell state, flow time, and a structured transition descriptor. Minibatch optimal transport (OT) supplies couplings only for conditional flow-matching training paths; inference requires neither target expression nor OT computation. On held-out donors, TempoBridge achieves an Energy distance of 0.129 versus 0.144 for scGen. Genetic mean-expression L_2 error is 2.261 versus 3.156 for scGPT-scratch under Seen 2/2. On held-out compounds, condition-averaged drug-effect correlation is 0.598 versus 0.561 for the CellFlow adapter. Temporal ablations show higher mean distributional error after removing source context, replacing optimal transport with random pairing, or replacing flow matching with static residual regression. Together, these results demonstrate the predictive utility of a common source-conditioned transport formulation across held-out donors, gene combinations, and compounds.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cyclically among prescribed velocity fields V_1,dots,V_p with random run times and evolves according to either a flight dynamics, consisting of piecewise-linear motion, or a gliding dynamics, in which the particle follows the corresponding velocity flow. Under a Kac-type scaling that couples vanishing run times with diverging particle speed, we prove weak convergence of both processes to multidimensional diffusions. It turns out that the order of successive cyclic motions affects the diffusion limit. In addition to the second-order term generated by fluctuations of the random run times, the limiting drift contains directional derivatives DV_i[V_j] of the underlying vector fields. In Stratonovich form, part of this drift is expressed through their Lie brackets [V_i,V_j]. Thus, the generic non-commutativity of the microscopic motions survives the diffusive scaling and generates a macroscopic drift which depends on the cyclic order. The limiting drift also distinguishes the flight and gliding dynamics, despite their being driven by the same vector fields and run times. Several examples, including run-and-reverse motion and cyclic dynamics generated by multiple vector fields, illustrate how the cyclic switching protocol and the geometry of the underlying velocity fields shape the limiting diffusions.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

In this paper, we explore osmotic transport by means of molecular dynamics (MD) simulations. We first consider osmosis through a membrane, and investigate the reflection coefficient of an imperfectly semi-permeable membrane, in the dilute and high concentration regimes. We then explore the diffusion-osmotic flow of a solute-solvent fluid adjacent to a solid surface, driven by a chemical potential gradient parallel to the surface. We propose a novel non-equilibrium MD (NEMD) methodology to simulate diffusion-osmosis, by imposing an external force on every particle, which properly mimics the chemical potential gradient on the solute in spite of the periodic boundary conditions. This NEMD method is validated theoretically on the basis of linear-response theory by matching the mobility with their Green-Kubo expressions. Finally, we apply the framework to more realistic systems, namely a water-ethanol mixture in contact with a silica or a graphene surface.

Phenotypic plasticity, the ability of cells to switch between states, is central to development, differentiation, and therapy resistance. Although it is modeled at several scales, from compartmental ODEs to phenotype-structured PDEs and single-cell stochastic equations, a framework connecting these descriptions is missing. We present such a framework. Starting from a general n-compartment ODE model encompassing nonlinear growth and linear transitions between phenotypes, we show, with a new, elementary and generalizable proof of a recent theorem, that under uniform competition, the long-term population distribution is solely governed by transition rates. All phenotypes become selectively neutral at saturation, and the imprint of fitness differences during growth fades at an explicit rate. Restricting transitions to neighboring states transforms the model into a discretization of a phenotype-structured reaction-diffusion-advection PDE. In this continuum model, diffusion and advection are identified from switching rates, and fitness remains asymptotically irrelevant. Interpreting the advection velocity as the negative gradient of an effective epigenetic potential transforms the PDE into a Fokker--Planck equation and converts single-cell trajectories into stochastic gradient descent (SGD) in the Langevin sense on the phenotypic landscape. Non-local transitions, such as mutations, are incorporated via an integro-differential term, yielding a unified model with reaction, gradient flow, diffusion, and jumps. State-dependent noise reshapes the effective landscape without altering the underlying potential. This gives cancer a route to elevated plasticity that static, single-cell snapshots cannot distinguish from a changed landscape. This framework provides a physical interpretation of Waddington's landscape, where cells perform SGD, and cancer corresponds to a corrupted landscape.

Human motion generation holds significant promise in fields such as animation, film production, and robotics. However, existing methods often fail to produce physically plausible movements that adhere to biomechanical principles. While recent autoregressive and diffusion models have improved visual quality, they frequently overlook essential biodynamic features, such as muscle activation patterns and joint coordination, leading to motions that either violate physical laws or lack controllability. This paper introduces BioMoDiffuse, a novel biomechanics-aware diffusion framework that addresses these limitations. It features three key innovations: (1) A lightweight biodynamic network that integrates muscle electromyography (EMG) signals and kinematic features with acceleration constraints, (2) A physics-guided diffusion process that incorporates real-time biomechanical verification via modified Euler-Lagrange equations, and (3) A decoupled control mechanism that allows independent regulation of motion speed and semantic context. We also propose a set of comprehensive evaluation protocols that combines traditional metrics (FID, R-precision, etc.) with new biomechanical criteria (smoothness, foot sliding, floating, etc.). Our approach bridges the gap between data-driven motion synthesis and biomechanical authenticity, establishing new benchmarks for physically accurate motion generation.

Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics and `decide' what to do, we propose a minimal axisymmetric model of a spherical active drop, and show that simple and linear interface properties can lead to both steady self-propulsion of the droplet as well as chaotic behavior. The model includes two different mobility mechanisms, namely, diffusiophoresis and the Marangoni effect, that convert self-generated gradients of surfactant concentration into the flow at the droplet surface. In turn, surface-driven flow initiates surfactant advection that is the only nonlinear mechanism and, thus, the only source of dynamical complexity in our model. Numerical investigation of the fully-coupled hydrodynamic and advection diffusion problems reveals that strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. Our results indicate that the thresholds of these instabilities depend heavily on the balance between diffusiophoresis and the Marangoni effect. Using linear stability analysis, we demonstrate that diffusiophoresis promotes the onset of high-order modes of monotonic instability of the motionless drop. We argue that diffusiophoresis has a similar effect on the instabilities of a moving drop.

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the intrinsic mutual interference among image regions contradicts the need for practical downstream application scenarios where the preservation of low-level pixel information from given conditioning is desired (e.g., customization tasks like personalized generation and inpainting based on a user-provided single image). In this work, we investigate the diffusion (physics) in diffusion (machine learning) properties and propose our Cyclic One-Way Diffusion (COW) method to control the direction of diffusion phenomenon given a pre-trained frozen diffusion model for versatile customization application scenarios, where the low-level pixel information from the conditioning needs to be preserved. Notably, unlike most current methods that incorporate additional conditions by fine-tuning the base text-to-image diffusion model or learning auxiliary networks, our method provides a novel perspective to understand the task needs and is applicable to a wider range of customization scenarios in a learning-free manner. Extensive experiment results show that our proposed COW can achieve more flexible customization based on strict visual conditions in different application settings. Project page: https://wangruoyu02.github.io/cow.github.io/.

As a powerful tool for characterizing cellular subpopulations and cellular heterogeneity, single cell RNA sequencing (scRNA-seq) technology offers advantages of high throughput and multidimensional analysis. However, the process of data acquisition is often constrained by high cost and limited sample availability. To overcome these limitations, we propose a hybrid model based on Diffusion model and White-Box transformer that aims to generate synthetic and biologically plausible scRNA-seq data. Diffusion model progressively introduce noise into the data and then recover the original data through a denoising process, a forward and reverse process that is particularly suitable for generating complex data distributions. White-Box transformer is a deep learning architecture that emphasizes mathematical interpretability. By minimizing the encoding rate of the data and maximizing the sparsity of the representation, it not only reduces the computational burden, but also provides clear insight into underlying structure. Our White-Box Diffusion Transformer combines the generative capabilities of Diffusion model with the mathematical interpretability of White-Box transformer. Through experiments using six different single-cell RNA-Seq datasets, we visualize both generated and real data using t-SNE dimensionality reduction technique, as well as quantify similarity between generated and real data using various metrics to demonstrate comparable performance of White-Box Diffusion Transformer and Diffusion Transformer in generating scRNA-seq data alongside significant improvements in training efficiency and resource utilization. Our code is available at https://github.com/lingximamo/White-Box-Diffusion-Transformer

Diffusion models have excelled at generative tasks for both continuous and token-based domains, but their application to discrete ordinal data remains underdeveloped. We present CountsDiff, a diffusion framework designed to model distributions on the natural numbers. CountsDiff extends the Blackout diffusion framework by simplifying its formulation through a direct parameterization in terms of a survival probability schedule and an explicit loss weighting. This introduces flexibility through design parameters with direct analogues in existing diffusion modeling frameworks. Beyond this reparameterization, CountsDiff introduces features from modern diffusion models, previously absent in counts-based domains, including continuous-time training, classifier-free guidance, and churn/remasking reverse dynamics that allow non-monotone reverse trajectories. We propose an initial instantiation of CountsDiff and validate it on natural image datasets (CIFAR-10, CelebA), exploring the effects of the introduced design parameters in a complex, well-studied, and interpretable data domain. We then highlight biological count assays as a natural use case, evaluating CountsDiff on single-cell RNA-seq imputation in fetal and heart cell atlases. Remarkably, we find that even this simple instantiation matches or surpasses the performance of a state-of-the-art discrete generative model and leading scRNA-seq imputation methods, while leaving substantial headroom for further gains through optimized design choices in future work.

Generative diffusion models have emerged as a powerful tool for high-quality image synthesis, yet their iterative nature demands significant computational resources. This paper proposes an efficient time step sampling method based on an image spectral analysis of the diffusion process, aimed at optimizing the denoising process. Instead of the traditional uniform distribution-based time step sampling, we introduce a Beta distribution-like sampling technique that prioritizes critical steps in the early and late stages of the process. Our hypothesis is that certain steps exhibit significant changes in image content, while others contribute minimally. We validated our approach using Fourier transforms to measure frequency response changes at each step, revealing substantial low-frequency changes early on and high-frequency adjustments later. Experiments with ADM and Stable Diffusion demonstrated that our Beta Sampling method consistently outperforms uniform sampling, achieving better FID and IS scores, and offers competitive efficiency relative to state-of-the-art methods like AutoDiffusion. This work provides a practical framework for enhancing diffusion model efficiency by focusing computational resources on the most impactful steps, with potential for further optimization and broader application.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes.

The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-trained diffusion models without incurring the significant computational burden of re-training a larger combined model. In this paper, we cast the problem of combining multiple pre-trained diffusion models at the generation stage under a novel proposed framework termed superposition. Theoretically, we derive superposition from rigorous first principles stemming from the celebrated continuity equation and design two novel algorithms tailor-made for combining diffusion models in SuperDiff. SuperDiff leverages a new scalable It\^o density estimator for the log likelihood of the diffusion SDE which incurs no additional overhead compared to the well-known Hutchinson's estimator needed for divergence calculations. We demonstrate that SuperDiff is scalable to large pre-trained diffusion models as superposition is performed solely through composition during inference, and also enjoys painless implementation as it combines different pre-trained vector fields through an automated re-weighting scheme. Notably, we show that SuperDiff is efficient during inference time, and mimics traditional composition operators such as the logical OR and the logical AND. We empirically demonstrate the utility of using SuperDiff for generating more diverse images on CIFAR-10, more faithful prompt conditioned image editing using Stable Diffusion, and improved unconditional de novo structure design of proteins. https://github.com/necludov/super-diffusion

Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

Fluorescence microscopy reveals where proteins localize, but only a limited number of proteins can be imaged in the same cell; generating these images from amino-acid sequence and the cell's morphological context enables in silico localization of unimaged proteins. The two conditions, however, play asymmetric roles: morphological context is spatially aligned with the target, whereas sequence is non-spatial and must specify protein-dependent localization within it, with recurring coarse patterns shared across proteins and finer protein-specific variation. Existing generators condition on both jointly, without separating what each explains. We introduce FACET (Factorized Asymmetric Conditioning for Efficient Transport), a probabilistic generative framework that encodes this structure as an explicit inductive bias: sequence semantics are learned from what context leaves unexplained, coarse localization regularities are shared across proteins through a semantic memory, and protein-specific variation is a bounded residual around them. A variance-preserving state projection further lets FACET perform continuous stochastic transport through a pretrained diffusion predictor with minimal parameter overhead. On held-out proteins, FACET improves spatial overlap by 34.3% on the Human Protein Atlas and 14.0% on OpenCell over a backbone-matched baseline, and reduces FID by 27.2% and 46.5%, respectively, with 75% fewer network evaluations. It also substantially improves protein-association structure recovery and yields better-calibrated predictions, while detailed ablations show complementary contributions from its design choices. These results identify factorized asymmetric conditioning, rather than generator capacity alone, as a key lever for high-fidelity, efficient, and biologically meaningful cellular image synthesis.

Cell tracking is a subject of active research gathering great interest in medicine and biology. Positron emission tomography (PET) is well suited for tracking radio-labeled cells in vivo due to its exceptional sensitivity and whole-body capability. For validation, ground-truth data are desirable that realistically mimic the flow of cells in a clinical situation. This study develops a workflow (CeFloPS) for simulating moving radio-labeled cells in a human phantom. From the XCAT phantom, the blood vessels are reduced to nodal networks along which cells can move and distribute to organs and tissues. The movement is directed by the blood flow, which is calculated in each node using the Hagen-Pooiseuille equation and Kirchhoff's laws assuming laminar flow. Organs are voxelized and movement of cells from artery entry to vein exit is generated via a biased 3D random walk. The probabilities of cells moving or remaining in tissues are derived from rate constants of tracer kinetic-based compartment modeling. PET listmode data is generated using the Monte-Carlo simulation framework GATE based on the definition of a large-body PET scanner with cell paths as moving radioactive sources and the XCAT phantom providing attenuation data. From the flow simulation of 100,000 cells, 100 sample cells were further processed by GATE and listmode data was reconstructed into images for comparison. As demonstrated by comparisons of simulated and reconstructed cell distributions, CeFloPS is capable of simulating cell behavior in whole-body PET. It achieves this simulation in a way that is anatomically and physiologically reasonable, thereby providing valuable data for the development and validation of cell tracking algorithms.

Single-cell cancer datasets are predominantly cross-sectional and rarely provide paired or longitudinal observations linking individual healthy-like cells to tumor-associated states. We introduce CancerZigZag, a seed-initialized diffusion-based framework for exploratory generation of tumor-associated single-cell candidate clouds from unpaired epithelial cell populations. For each cancer context, a diffusion model is trained exclusively on tumor-derived epithelial cells and applied through repeated partial latent-space perturbation and reverse diffusion to held-out healthy-like seeds, generating stochastic candidate clouds without paired measurements or classifier guidance. We applied CancerZigZag to colorectal, breast, lung, and renal cell carcinoma contexts and explored parameter landscapes defined by perturbation depth and the number of ZigZag cycles. Across the reported operating configurations, candidate clouds contained outputs classified toward held-out tumor-derived reference populations for each evaluated seed. Residual seed-dependent organization varied across contexts, with the clearest structure in colorectal cancer, more modest organization in lung cancer, and limited cloud-level structure in breast and renal cell carcinoma. Representative candidates also showed directional concordance with transcriptional shifts observed between held-out healthy-like and tumor-derived reference populations. CancerZigZag is not interpreted as a model of deterministic healthy-to-tumor transformation or cellular progression. Instead, it provides a reference-informed framework for exploring tumor-associated candidate distributions from unpaired healthy-like seeds and quantifying the context-dependent relationship between tumor-associated displacement and residual seed dependence.

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.

We introduce a technique for extracting microstructural geometry from NMR lineshape analysis in porous materials at angstrom-scale resolution with the use of weak magnetic field gradients. Diverging from the generally held view of FID signals undergoing simple exponential decay, we show that a detailed analysis of the line shape can unravel structural geometry on much smaller scales than previously thought. While the original q-space PFG NMR relies on strong magnetic field gradients in order to achieve high spatial resolution, our current approach reaches comparable or higher resolution using much weaker gradients. As a model system, we simulated gas diffusion for xenon confined within carbon nanotubes over a range of temperatures and nanotube diameters in order to unveil manifestations of confinement in the diffusion behavior. We report a multiscale scheme that couples the above MD simulations with the generalized Langevin equation to estimate the transport properties of interest for this problem, such as diffusivity coefficients and NMR lineshapes, using the Green-Kubo correlation function to correctly evaluate time-dependent diffusion. Our results highlight how NMR methodologies can be adapted as effective means towards structural investigation at very small scales when dealing with complicated geometries. This method is expected to find applications in materials science, catalysis, biomedicine and other areas.

Building Virtual Cells that can accurately simulate cellular responses to perturbations is a long-standing goal in systems biology. A fundamental challenge is that high-throughput single-cell sequencing is destructive: the same cell cannot be observed both before and after a perturbation. Thus, perturbation prediction requires mapping unpaired control and perturbed populations. Existing models address this by learning maps between distributions, but typically assume a single fixed response distribution when conditioned on observed cellular context (e.g., cell type) and the perturbation type. In reality, responses vary systematically due to unobservable latent factors such as microenvironmental fluctuations and complex batch effects, forming a manifold of possible distributions for the same observed conditions. To account for this variability, we introduce PerturbDiff, which shifts modeling from individual cells to entire distributions. By embedding distributions as points in a Hilbert space, we define a diffusion-based generative process operating directly over probability distributions. This allows PerturbDiff to capture population-level response shifts across hidden factors. Benchmarks on established datasets show that PerturbDiff achieves state-of-the-art performance in single-cell response prediction and generalizes substantially better to unseen perturbations. See our project page (https://katarinayuan.github.io/PerturbDiff-ProjectPage/), where code and data will be made publicly available (https://github.com/DeepGraphLearning/PerturbDiff).

Echocardiography has been a prominent tool for the diagnosis of cardiac disease. However, these diagnoses can be heavily impeded by poor image quality. Acoustic clutter emerges due to multipath reflections imposed by layers of skin, subcutaneous fat, and intercostal muscle between the transducer and heart. As a result, haze and other noise artifacts pose a real challenge to cardiac ultrasound imaging. In many cases, especially with difficult-to-image patients such as patients with obesity, a diagnosis from B-Mode ultrasound imaging is effectively rendered unusable, forcing sonographers to resort to contrast-enhanced ultrasound examinations or refer patients to other imaging modalities. Tissue harmonic imaging has been a popular approach to combat haze, but in severe cases is still heavily impacted by haze. Alternatively, denoising algorithms are typically unable to remove highly structured and correlated noise, such as haze. It remains a challenge to accurately describe the statistical properties of structured haze, and develop an inference method to subsequently remove it. Diffusion models have emerged as powerful generative models and have shown their effectiveness in a variety of inverse problems. In this work, we present a joint posterior sampling framework that combines two separate diffusion models to model the distribution of both clean ultrasound and haze in an unsupervised manner. Furthermore, we demonstrate techniques for effectively training diffusion models on radio-frequency ultrasound data and highlight the advantages over image data. Experiments on both in-vitro and in-vivo cardiac datasets show that the proposed dehazing method effectively removes haze while preserving signals from weakly reflected tissue.

Large-scale, pre-trained Text-to-Image (T2I) diffusion models have gained significant popularity in image generation tasks and have shown unexpected potential in image Super-Resolution (SR). However, most existing T2I diffusion models are trained with a resolution limit of 512x512, making scaling beyond this resolution an unresolved but necessary challenge for image SR. In this work, we introduce a novel approach that, for the first time, enables these models to generate 2K, 4K, and even 8K images without any additional training. Our method leverages MultiDiffusion, which distributes the generation across multiple diffusion paths to ensure global coherence at larger scales, and local degradation-aware prompt extraction, which guides the T2I model to reconstruct fine local structures according to its low-resolution input. These innovations unlock higher resolutions, allowing T2I diffusion models to be applied to image SR tasks without limitation on resolution.

Learning a transport model that maps a source distribution to a target distribution is a canonical problem in machine learning, but scientific applications increasingly require models that can generalize to source and target distributions unseen during training. We introduce distribution-conditioned transport (DCT), a framework that conditions transport maps on learned embeddings of source and target distributions, enabling generalization to unseen distribution pairs. DCT also allows semi-supervised learning for distributional forecasting problems: because it learns from arbitrary distribution pairs, it can leverage distributions observed at only one condition to improve transport prediction. DCT is agnostic to the underlying transport mechanism, supporting models ranging from flow matching to distributional divergence-based models (e.g. Wasserstein, MMD). We demonstrate the practical performance benefits of DCT on synthetic benchmarks and four applications in biology: batch effect transfer in single-cell genomics, perturbation prediction from mass cytometry data, learning clonal transcriptional dynamics in hematopoiesis, and modeling T-cell receptor sequence evolution.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Genetic engineering of cells has a range of applications in treating incurable diseases. Plasmid DNA is a popular choice of nucleic acid for cell engineering due to its low cost and stability. However, plasmid DNA must survive the protective mechanisms present in the cell's cytoplasm to enter the nucleus for translation. Many of the existing methods for nucleic acid delivery, such as chemical-based and virus-based delivery, suffer from drawbacks induced by the nucleic acid carrier itself. Mechanical methods present an alternative to nucleic acid carriers by physically producing openings in the cell to deliver cargos. However, in most systems, the cell membrane openings are too small to deliver large cargos, or the poration process leads to low cell viability. In this study, we present a microfluidic device with integrated high aspect ratio nanostructures that repeatably rupture the cell membrane and nuclear envelope. These sharp-tipped nanolancets penetrate the cell deep enough to allow direct delivery of cargos into the nucleus, but still allow for cell recovery after treatment. We show the device's ability to deliver cargo to a variety of cell types while maintaining high viability. Then, we demonstrate the rapid onset of plasmid DNA expression that results from direct nuclear delivery of naked DNA, showing expression speeds comparable to microinjection, but with significantly greater throughput. We envision the use of this device as a tool to quickly produce high quantities of genetically engineered cells to treat a myriad of diseases.

Biomedical datasets are often constrained by stringent privacy requirements and frequently suffer from severe class imbalance. These two aspects hinder the development of accurate machine learning models. While generative AI offers a promising solution, producing synthetic images of sufficient quality for training robust classifiers remains challenging. This work addresses the classification of individual white blood cells, a critical task in diagnosing hematological malignancies such as acute myeloid leukemia (AML). We introduce CytoDiff, a stable diffusion model fine-tuned with LoRA weights and guided by few-shot samples that generates high-fidelity synthetic white blood cell images. Our approach demonstrates substantial improvements in classifier performance when training data is limited. Using a small, highly imbalanced real dataset, the addition of 5,000 synthetic images per class improved ResNet classifier accuracy from 27\% to 78\% (+51\%). Similarly, CLIP-based classification accuracy increased from 62\% to 77\% (+15\%). These results establish synthetic image generation as a valuable tool for biomedical machine learning, enhancing data coverage and facilitating secure data sharing while preserving patient privacy. Paper code is publicly available at https://github.com/JanCarreras24/CytoDiff.

Reparameterized diffusion models (RDMs) have recently matched autoregressive methods in protein generation, motivating their use for challenging tasks such as designing membrane proteins, which possess interleaved soluble and transmembrane (TM) regions. We introduce the Membrane Diffusion Language Model (MemDLM), a fine-tuned RDM-based protein language model that enables controllable membrane protein sequence design. MemDLM-generated sequences recapitulate the TM residue density and structural features of natural membrane proteins, achieving comparable biological plausibility and outperforming state-of-the-art diffusion baselines in motif scaffolding tasks by producing lower perplexity, higher BLOSUM-62 scores, and improved pLDDT confidence. To enhance controllability, we develop Per-Token Guidance (PET), a novel classifier-guided sampling strategy that selectively solubilizes residues while preserving conserved TM domains, yielding sequences with reduced TM density but intact functional cores. Importantly, MemDLM designs validated in TOXCAT beta-lactamase growth assays demonstrate successful TM insertion, distinguishing high-quality generated sequences from poor ones. Together, our framework establishes the first experimentally-validated diffusion-based model for rational membrane protein generation, integrating de novo design, motif scaffolding, and targeted property optimization.

We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality.

Recent advances in Conditional Diffusion Models have led to substantial capabilities in various domains. However, understanding the impact of variations in the initial seed vector remains an underexplored area of concern. Particularly, latent-based diffusion models display inconsistencies in image generation under standard conditions when initialized with suboptimal initial seed vectors. To understand the impact of the initial seed vector on generated samples, we propose a reliability evaluation framework that evaluates the generated samples of a diffusion model when the initial seed vector is subjected to various synthetic shifts. Our results indicate that slight manipulations to the initial seed vector of the state-of-the-art Stable Diffusion (Rombach et al., 2022) can lead to significant disturbances in the generated samples, consequently creating images without the effect of conditioning variables. In contrast, GLIDE (Nichol et al., 2022) stands out in generating reliable samples even when the initial seed vector is transformed. Thus, our study sheds light on the importance of the selection and the impact of the initial seed vector in the latent-based diffusion model.

We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the applied difference of potential and the current across the cell. We show that in the case of anomalous diffusion, the model predicts for the electric impedance of the cell a constant phase element behaviour in the low frequency region. In the parametric curve of the reactance versus the resistance, the slope coincides with the order of the fractional time derivative.

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose \textbf{Multi-Marginal temporal Schr\"odinger Bridge Matching} (MMtSBM) for video generation from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schr\"odinger Bridge Matching (arXiv:archive/2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real world datasets such as transcriptomic trajectory inference in 100 dimensions, and for the first time recovers couplings and dynamics in very high dimensional image settings. Our work establishes multi-marginal Schr\"odinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

The diffusion MRI Neurite Exchange Imaging model offers a promising framework for probing gray matter microstructure by estimating parameters such as compartment sizes, diffusivities, and inter-compartmental water exchange time. However, existing protocols require long scan times. This study proposes a reduced acquisition scheme for the Connectome 2.0 scanner that preserves model accuracy while substantially shortening scan duration. We developed a data-driven framework using explainable artificial intelligence with a guided recursive feature elimination strategy to identify an optimal 8-feature subset from a 15-feature protocol. The performance of this optimized protocol was validated in vivo and benchmarked against the full acquisition and alternative reduction strategies. Parameter accuracy, preservation of anatomical contrast, and test-retest reproducibility were assessed. The reduced protocol yielded parameter estimates and cortical maps comparable to the full protocol, with low estimation errors in synthetic data and minimal impact on test-retest variability. Compared to theory-driven and heuristic reduction schemes, the optimized protocol demonstrated superior robustness, reducing the deviation in water exchange time estimates by over two-fold. In conclusion, this hybrid optimization framework enables viable imaging of neurite exchange in 14 minutes without loss of parameter fidelity. This approach supports the broader application of exchange-sensitive diffusion magnetic resonance imaging in neuroscience and clinical research, and offers a generalizable method for designing efficient acquisition protocols in biophysical parameter mapping.

Despite significant progress in generative modelling, existing diffusion models often struggle to produce anatomically precise female pelvic images, limiting their application in gynaecological imaging, where data scarcity and patient privacy concerns are critical. To overcome these barriers, we introduce a novel diffusion-based framework for uterine MRI synthesis, integrating both unconditional and conditioned Denoising Diffusion Probabilistic Models (DDPMs) and Latent Diffusion Models (LDMs) in 2D and 3D. Our approach generates anatomically coherent, high fidelity synthetic images that closely mimic real scans and provide valuable resources for training robust diagnostic models. We evaluate generative quality using advanced perceptual and distributional metrics, benchmarking against standard reconstruction methods, and demonstrate substantial gains in diagnostic accuracy on a key classification task. A blinded expert evaluation further validates the clinical realism of our synthetic images. We release our models with privacy safeguards and a comprehensive synthetic uterine MRI dataset to support reproducible research and advance equitable AI in gynaecology.

In this paper, we prove the existence of stationary pulse solutions for a bulk-surface reaction-diffusion system modeling cell polarization in two-dimensional domains. Using a singular perturbation method, we construct pulse solutions whose centers lie near non-degenerate critical points of a geometry-dependent potential expressed in terms of the Neumann Green's function, as formally predicted in watanabe2026. The main analytical difficulty arises from the half-Laplacian induced by the logarithmic singularity of the Green's function, resulting in algebraically rather than exponentially decaying inner solutions. Our analysis may also serve as a useful guide for applying singular perturbation methods to other bulk-surface type systems.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

Diffusion probabilistic models (DPMs) which employ explicit likelihood characterization and a gradual sampling process to synthesize data, have gained increasing research interest. Despite their huge computational burdens due to the large number of steps involved during sampling, DPMs are widely appreciated in various medical imaging tasks for their high-quality and diversity of generation. Magnetic resonance imaging (MRI) is an important medical imaging modality with excellent soft tissue contrast and superb spatial resolution, which possesses unique opportunities for DPMs. Although there is a recent surge of studies exploring DPMs in MRI, a survey paper of DPMs specifically designed for MRI applications is still lacking. This review article aims to help researchers in the MRI community to grasp the advances of DPMs in different applications. We first introduce the theory of two dominant kinds of DPMs, categorized according to whether the diffusion time step is discrete or continuous, and then provide a comprehensive review of emerging DPMs in MRI, including reconstruction, image generation, image translation, segmentation, anomaly detection, and further research topics. Finally, we discuss the general limitations as well as limitations specific to the MRI tasks of DPMs and point out potential areas that are worth further exploration.

A central statistical problem in population genetics is to infer evolutionary and biological parameters such as the strength of natural selection and allele age from DNA samples extracted from a contemporary population. That all samples come only from the present-day has long been known to limit statistical inference; there is potentially more information available if one also has access to ancient DNA so that inference is based on a time-series of historical changes in allele frequencies. We introduce a Markov Chain Monte Carlo (MCMC) method for Bayesian inference from allele frequency time-series data based on an underlying Wright--Fisher diffusion model of evolution, through which one can infer the parameters of essentially any selection model including those with frequency-dependent effects. The chief novelty is that we show this method to be exact in the sense that it is possible to augment the state space explored by MCMC with the unobserved diffusion trajectory, even though the transition function of this diffusion is intractable. Through careful design of a proposal distribution, we describe an efficient method in which updates to the trajectory and accept/reject decisions are calculated without error. We illustrate the method on data capturing changes in coat colour over the past 20,000 years, and find evidence to support previous findings that the mutant alleles ASIP and MC1R responsible for changes in coat color have experienced very strong, possibly overdominant, selection and further provide estimates for the ages of these genes.

A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the clusters. It is shown that thermal diffusion emerges in the collective description as a significant factor even if it is negligible when transport of the original molecular species is considered. Analytical expressions for the effective diffusion and thermal diffusion coefficients at temperature, pressure, and chemical composition gradients have been derived. The theory has been applied to a technology of H2S conversion in a centrifugal plasma-chemical reactor and has made it possible to account for sulfur clusters in numerical process modeling.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

A hybrid kinetic-fluid model is used to study plasma stratification in alternating current (AC) discharges in noble gases at low plasma densities. Self-consistent coupled solutions of a nonlocal kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained for a positive column and the entire discharge with near-electrode sheaths. A simplified two-level excitation-ionization model neglects the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons. Standing striations are obtained for the reduced values of electric fields, E/p, corresponding to the inelastic energy balance of electrons in a range of driving frequencies. An analog of Novak law (striation length proportional to the excitation threshold of atoms and inversely proportional to the mean square root of the electric field), is observed in simulations, indicating the nonlocal nature of standing striations in AC discharges at low plasma densities. Stratified plasma operates in a dynamic regime for various driving frequencies. In this regime, ions respond to the time-averaged electric field, whereas electrons react to the instantaneous electric field. The disparity of time scales between ambipolar diffusion, which occurs at the ion time scale, and electron kinetics in the coordinate-energy phase space, which occurs at the free electron diffusion time scale, produces complicated fluxes in the phase space (due to electron heating, energy loss in collisions, and ionization processes) that are responsible for the stratification. Our paper emphasizes the need for the kinetic approach to analyze stratification phenomena in AC discharge of noble gases. It promotes an efficient method for the kinetic treatment of electrons that is an alternative to the commonly used PIC method.

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on R^n defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Gamma-convergence for pairs of phase functions (u_varepsilon,v_varepsilon). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disease. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

Modeling cellular states and predicting their responses to perturbations are central challenges in computational biology and the development of virtual cells. Existing foundation models for single-cell transcriptomics provide powerful static representations, but they do not explicitly model the distribution of cellular states for generative simulation. Here, we introduce Lingshu-Cell, a masked discrete diffusion model that learns transcriptomic state distributions and supports conditional simulation under perturbation. By operating directly in a discrete token space that is compatible with the sparse, non-sequential nature of single-cell transcriptomic data, Lingshu-Cell captures complex transcriptome-wide expression dependencies across approximately 18,000 genes without relying on prior gene selection, such as filtering by high variability or ranking by expression level. Across diverse tissues and species, Lingshu-Cell accurately reproduces transcriptomic distributions, marker-gene expression patterns and cell-subtype proportions, demonstrating its ability to capture complex cellular heterogeneity. Moreover, by jointly embedding cell type or donor identity with perturbation, Lingshu-Cell can predict whole-transcriptome expression changes for novel combinations of identity and perturbation. It achieves leading performance on the Virtual Cell Challenge H1 genetic perturbation benchmark and in predicting cytokine-induced responses in human PBMCs. Together, these results establish Lingshu-Cell as a flexible cellular world model for in silico simulation of cell states and perturbation responses, laying the foundation for a new paradigm in biological discovery and perturbation screening.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell death. The model accounts for spatial heterogeneity in both tumor cell density and drug concentration while capturing the complex dynamics of drug resistance development. We first establish the well-posedness of the coupled system by proving the existence and uniqueness of a solution under appropriate regularity conditions. The optimal control problem is then formulated to minimize tumor size while accounting for drug toxicity constraints. Using variational methods, we derive the necessary optimality conditions and characterize the optimal control through an adjoint system. Theoretical results can help to design effective chemotherapy schedules that balance treatment efficacy with adverse effects.

Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are computationally expensive, requiring many neural function evaluations (NFEs). In this work, we propose an anytime diffusion-based method that can generate viable images when stopped at arbitrary times before completion. Using existing pretrained diffusion models, we show that the generation scheme can be recomposed as two nested diffusion processes, enabling fast iterative refinement of a generated image. We use this Nested Diffusion approach to peek into the generation process and enable flexible scheduling based on the instantaneous preference of the user. In experiments on ImageNet and Stable Diffusion-based text-to-image generation, we show, both qualitatively and quantitatively, that our method's intermediate generation quality greatly exceeds that of the original diffusion model, while the final slow generation result remains comparable.

Generating accurate 3D molecules requires jointly determining a variable number of atoms, their identities, and geometry across spatial scales: global shape emerges coarsely, whereas chemical bonds demand fine local precision. Existing atom-based diffusion and flow models operate largely at a single scale, while dense spatial fields become costly at high resolution. We introduce OctMole, a multiscale octree flow framework for 3D molecular generation. A hierarchical occupancy flow progressively resolves sparse molecular support from coarse to fine, and a joint atom flow assigns atom types and continuous in-cell offsets to occupied leaves. This decomposition combines efficient global structure with subcell geometric precision, while cell corruption improves robustness to generated support. On QM9 and GEOM-DRUG, OctMole achieves strong chemical, distributional, and geometric quality, with particularly clear gains over Uni-3DAR on GEOM-DRUG and substantial efficiency gains over dense 3D generation. As an additional capability, intermediate occupancy states and selected regions provide spatial conditioning without task-specific retraining, supporting multiscale shape conditioning, regional editing, linker generation, and shape interpolation. Code and pretrained checkpoints are available at https://github.com/octree-nn/octmole and https://huggingface.co/Disembo/octmole, respectively.

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of large-scale image repositories in biology and recent advances in generative modeling, there is an opportunity to accelerate the discovery of evolutionary traits automatically from images. Toward this goal, we introduce Phylo-Diffusion, a novel framework for conditioning diffusion models with phylogenetic knowledge represented in the form of HIERarchical Embeddings (HIER-Embeds). We also propose two new experiments for perturbing the embedding space of Phylo-Diffusion: trait masking and trait swapping, inspired by counterpart experiments of gene knockout and gene editing/swapping. Our work represents a novel methodological advance in generative modeling to structure the embedding space of diffusion models using tree-based knowledge. Our work also opens a new chapter of research in evolutionary biology by using generative models to visualize evolutionary changes directly from images. We empirically demonstrate the usefulness of Phylo-Diffusion in capturing meaningful trait variations for fishes and birds, revealing novel insights about the biological mechanisms of their evolution.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

Text-to-image diffusion models produce high quality images but do not offer control over individual instances in the image. We introduce InstanceDiffusion that adds precise instance-level control to text-to-image diffusion models. InstanceDiffusion supports free-form language conditions per instance and allows flexible ways to specify instance locations such as simple single points, scribbles, bounding boxes or intricate instance segmentation masks, and combinations thereof. We propose three major changes to text-to-image models that enable precise instance-level control. Our UniFusion block enables instance-level conditions for text-to-image models, the ScaleU block improves image fidelity, and our Multi-instance Sampler improves generations for multiple instances. InstanceDiffusion significantly surpasses specialized state-of-the-art models for each location condition. Notably, on the COCO dataset, we outperform previous state-of-the-art by 20.4% AP_{50}^box for box inputs, and 25.4% IoU for mask inputs.

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the extreme near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the near-contact limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the capsize determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

Scientific measurements such as single-cell RNA (scRNA) sequencing often take the form of nonnegative integer counts, whereas continuous-state diffusion models approximate this discrete structure using continuous coordinates. Building on stochastic chemical reaction networks (CRNs), a class of count-native Markov jump processes, we introduce CRNDiff, a structured framework that combines count-space diffusion with inference-time conditioning on rare subpopulations. An independent birth--death instantiation yields a closed-form transition kernel for forward noising. This kernel enables reverse sampling via forward-filtering backward-sampling (FFBS) and supports data-driven selection of the terminal noising time, eliminating the need for a validation sweep. This tractability also lets us introduce tilted Feynman--Kac (FK) steering, a method for sampling target subpopulations from a frozen generator without retraining. By tilting posterior marginals before FK particle correction, steering mitigates importance-weight concentration when the target population is rare. Using scRNA-seq data from the human heart cell atlas, we test the ability of CRNDiff to generate cell-type-specific distributions. Across the three evaluated target populations, CRNDiff achieves the highest conditional fidelity among the evaluated generative models, with larger mean purity margins for rarer target populations. Generated cells preserve marker-level differential-expression structure. Replacing real training cells for the target classes with generated cells yields downstream classification performance approaching that of the real-data reference.

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered are Ca^{2+} waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca^{2+} momentum, p. The canonical momentum of a charged particle in an electromagnetic field, mathbfΠ = p + q A (SI units), is calculated, where the charge of Ca^{2+} is q = - 2 e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca^{2+} ions, in both classical and quantum mechanics. Molecular scales of Ca^{2+} wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca^{2+} waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p + q A interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.

Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the lack of a regular and explicit grid structure also makes it challenging to apply generative modeling directly on implicit neural fields in order to synthesize new data. To this end, we propose HyperDiffusion, a novel approach for unconditional generative modeling of implicit neural fields. HyperDiffusion operates directly on MLP weights and generates new neural implicit fields encoded by synthesized MLP parameters. Specifically, a collection of MLPs is first optimized to faithfully represent individual data samples. Subsequently, a diffusion process is trained in this MLP weight space to model the underlying distribution of neural implicit fields. HyperDiffusion enables diffusion modeling over a implicit, compact, and yet high-fidelity representation of complex signals across 3D shapes and 4D mesh animations within one single unified framework.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

The deployment of large-scale text-to-image diffusion models on mobile devices is impeded by their substantial model size and slow inference speed. In this paper, we propose MobileDiffusion, a highly efficient text-to-image diffusion model obtained through extensive optimizations in both architecture and sampling techniques. We conduct a comprehensive examination of model architecture design to reduce redundancy, enhance computational efficiency, and minimize model's parameter count, while preserving image generation quality. Additionally, we employ distillation and diffusion-GAN finetuning techniques on MobileDiffusion to achieve 8-step and 1-step inference respectively. Empirical studies, conducted both quantitatively and qualitatively, demonstrate the effectiveness of our proposed techniques. MobileDiffusion achieves a remarkable sub-second inference speed for generating a 512times512 image on mobile devices, establishing a new state of the art.

Generative models have the potential to accelerate key steps in the discovery of novel molecular therapeutics and materials. Diffusion models have recently emerged as a powerful approach, excelling at unconditional sample generation and, with data-driven guidance, conditional generation within their training domain. Reliably sampling from high-value regions beyond the training data, however, remains an open challenge -- with current methods predominantly focusing on modifying the diffusion process itself. In this paper, we develop context-guided diffusion (CGD), a simple plug-and-play method that leverages unlabeled data and smoothness constraints to improve the out-of-distribution generalization of guided diffusion models. We demonstrate that this approach leads to substantial performance gains across various settings, including continuous, discrete, and graph-structured diffusion processes with applications across drug discovery, materials science, and protein design.

Ultrafast electron microscopy (UEM) has found widespread applications in physics, chemistry, and materials science, enabling real-space imaging of dynamics on ultrafast timescales. Recent advances have pushed the temporal resolution of UEM into the attosecond regime, enabling the attomicroscopy technique to directly visualize electron motion. In this work, we extend the capabilities of this powerful imaging tool to investigate ultrafast electron dynamics in a biological system by imaging and controlling light induced electronic and chemical changes in the conductive network of multicellular cable bacteria. Using electron energy loss spectroscopy (EELS), we first observed a laser induced increase in {\pi}-electron density, accompanied by spectral peak broadening and a blueshift features indicative of enhanced conductivity and structural modification. We also traced the effect of ultrafast laser pumping on bulk plasmon electron oscillations by monitoring changes in the plasmon like resonance peak. Additionally, we visualized laser induced chemical structural changes in cable bacteria in real space. The imaging results revealed carbon enrichment alongside a depletion of nitrogen and oxygen, highlighting the controllability of chemical dynamics. Moreover, time resolved EELS measurements further revealed a picosecond scale decay and recovery of both {\pi}-electron and plasmonic features, attributed to electron phonon coupling. In addition to shedding light on the mechanism of electron motion in cable bacteria, these findings demonstrate ultrafast modulation and switching of conductivity, underscoring their potential as bio-optoelectronic components operating on ultrafast timescales.

Diffusion-based image super-resolution (SR) methods are mainly limited by the low inference speed due to the requirements of hundreds or even thousands of sampling steps. Existing acceleration sampling techniques inevitably sacrifice performance to some extent, leading to over-blurry SR results. To address this issue, we propose a novel and efficient diffusion model for SR that significantly reduces the number of diffusion steps, thereby eliminating the need for post-acceleration during inference and its associated performance deterioration. Our method constructs a Markov chain that transfers between the high-resolution image and the low-resolution image by shifting the residual between them, substantially improving the transition efficiency. Additionally, an elaborate noise schedule is developed to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experiments demonstrate that the proposed method obtains superior or at least comparable performance to current state-of-the-art methods on both synthetic and real-world datasets, even only with 15 sampling steps. Our code and model are available at https://github.com/zsyOAOA/ResShift.

Diffusion models have achieved remarkable success across various domains. However, their slow generation speed remains a critical challenge. Existing acceleration methods, while aiming to reduce steps, often compromise sample quality, controllability, or introduce training complexities. Therefore, we propose RayFlow, a novel diffusion framework that addresses these limitations. Unlike previous methods, RayFlow guides each sample along a unique path towards an instance-specific target distribution. This method minimizes sampling steps while preserving generation diversity and stability. Furthermore, we introduce Time Sampler, an importance sampling technique to enhance training efficiency by focusing on crucial timesteps. Extensive experiments demonstrate RayFlow's superiority in generating high-quality images with improved speed, control, and training efficiency compared to existing acceleration techniques.

Recent advances in text-to-image generation with diffusion models present transformative capabilities in image quality. However, user controllability of the generated image, and fast adaptation to new tasks still remains an open challenge, currently mostly addressed by costly and long re-training and fine-tuning or ad-hoc adaptations to specific image generation tasks. In this work, we present MultiDiffusion, a unified framework that enables versatile and controllable image generation, using a pre-trained text-to-image diffusion model, without any further training or finetuning. At the center of our approach is a new generation process, based on an optimization task that binds together multiple diffusion generation processes with a shared set of parameters or constraints. We show that MultiDiffusion can be readily applied to generate high quality and diverse images that adhere to user-provided controls, such as desired aspect ratio (e.g., panorama), and spatial guiding signals, ranging from tight segmentation masks to bounding boxes. Project webpage: https://multidiffusion.github.io

Three-dimensional microscopy is often limited by anisotropic spatial resolution, resulting in lower axial resolution than lateral resolution. Current State-of-The-Art (SoTA) isotropic reconstruction methods utilizing deep neural networks can achieve impressive super-resolution performance in fixed imaging settings. However, their generality in practical use is limited by degraded performance caused by artifacts and blurring when facing unseen anisotropic factors. To address these issues, we propose DiffuseIR, an unsupervised method for isotropic reconstruction based on diffusion models. First, we pre-train a diffusion model to learn the structural distribution of biological tissue from lateral microscopic images, resulting in generating naturally high-resolution images. Then we use low-axial-resolution microscopy images to condition the generation process of the diffusion model and generate high-axial-resolution reconstruction results. Since the diffusion model learns the universal structural distribution of biological tissues, which is independent of the axial resolution, DiffuseIR can reconstruct authentic images with unseen low-axial resolutions into a high-axial resolution without requiring re-training. The proposed DiffuseIR achieves SoTA performance in experiments on EM data and can even compete with supervised methods.

Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish quantitative principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

Image enhancement finds wide-ranging applications in real-world scenarios due to complex environments and the inherent limitations of imaging devices. Recent diffusion-based methods yield promising outcomes but necessitate prolonged and computationally intensive iterative sampling. In response, we propose InstaRevive, a straightforward yet powerful image enhancement framework that employs score-based diffusion distillation to harness potent generative capability and minimize the sampling steps. To fully exploit the potential of the pre-trained diffusion model, we devise a practical and effective diffusion distillation pipeline using dynamic control to address inaccuracies in updating direction during score matching. Our control strategy enables a dynamic diffusing scope, facilitating precise learning of denoising trajectories within the diffusion model and ensuring accurate distribution matching gradients during training. Additionally, to enrich guidance for the generative power, we incorporate textual prompts via image captioning as auxiliary conditions, fostering further exploration of the diffusion model. Extensive experiments substantiate the efficacy of our framework across a diverse array of challenging tasks and datasets, unveiling the compelling efficacy and efficiency of InstaRevive in delivering high-quality and visually appealing results. Code is available at https://github.com/EternalEvan/InstaRevive.

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.

Familial amyloid-β (Aβ) variants alter aggregation kinetics, but their interaction with structural brain connectivity remains incompletely understood. We developed a mutation-aware mechanistic model coupling a coarse-grained monomer--oligomer--fibril aggregation--fragmentation system to graph diffusion on the 540-node Budapest Reference Connectome component. Experimental Aβ_{42} nucleation scores scaled primary nucleation rates for seven variants relative to wild type. Robustness was examined using mutation-score uncertainty, alternative kinetic mappings, global sensitivity analysis, seed and edge-weight perturbations, degree-preserving randomized connectomes, spatial propagation analysis, synthetic ABC-SMC parameter recovery, posterior prediction, and Chemical Langevin simulations. E22G showed the earliest threshold crossing and greatest cumulative oligomer burden, whereas A2V was delayed under the selected mapping. Mutation rankings persisted across tested network perturbations, although regional burden patterns depended on topology. Connectome distance from seed regions was associated with later oligomer arrival (Spearman ρapprox0.92). Under inferred parameter uncertainty, the mean timing-rank correlation was 0.990 and cumulative-burden ordering was preserved in every posterior draw, while exact peak-amplitude ordering was less stable. Stochastic ensemble medians retained the deterministic ordering despite overlap among trajectories. Within this proof-of-concept framework, mutation-dependent kinetics primarily influence aggregation timing and cumulative burden, while connectivity shapes spatial propagation. Nominal background rates, model-time units, and synthetic parameter recovery limit interpretation to mechanistic comparisons rather than clinically calibrated prediction.

Single-cell RNA-seq profiles are high-dimensional, sparse, and unordered, causing autoregressive generation to impose an artificial ordering bias and suffer from error accumulation. To address this, we propose scDiVa, a masked discrete diffusion foundation model that aligns generation with the dropout-like corruption process by defining a continuous-time forward masking mechanism in token space. ScDiVa features a bidirectional denoiser that jointly models discrete gene identities and continuous values, utilizing entropy-normalized serialization and a latent anchor token to maximize information efficiency and preserve global cell identity. The model is trained via depth-invariant time sampling and a dual denoising objective to simulate varying sparsity levels while ensuring precise recovery of both identity and magnitude. Pre-trained on 59 million cells, scDiVa achieves strong transfer performance across major benchmarks, including batch integration, cell type annotation, and perturbation response prediction. These results suggest that masked discrete diffusion serves as a biologically coherent and effective alternative to autoregression.

Inferring cellular dynamics from unpaired single-cell snapshots requires modeling both state transitions and population growth or death. Unbalanced dynamic optimal transport (UDOT) addresses this by penalizing growth along transport paths, making the choice of growth penalty a key way to encode biological priors on proliferation and apoptosis. However, existing UDOT solvers either rely on computationally expensive NeuralODE simulations or depend on analytical solutions of conditional paths, restricting their efficiency solely to quadratic penalties, i.e. Wasserstein-Fisher-Rao (WFR) geodesics. To enable an efficient UDOT solver for general growth penalties, we first show that concave growth penalties lead to degenerate solutions where growth and transport are separated. We then introduce Simulation-free Unbalanced Dynamic Optimal transport (SUDO), a simulation-free framework for UDOT with general non-quadratic convex growth penalties. SUDO learns the conditional paths and transport costs, solves the induced semi-coupling problem, and subsequently leverages unbalanced flow matching to achieve a simulation-free solution. On WFR benchmarks, SUDO matches the accuracy of efficient, analytical solution-driven algorithms while outperforming simulation-based methods in computational speed. Beyond WFR, SUDO supports asymmetric penalties that encode proliferation-dominant priors and produce more plausible trajectories and growth estimates on synthetic and single-cell datasets.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor - much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

Artificially synthesized Janus particles have tremendous prospective as in-vivo drug-delivery agents due to the possibility of self-propulsion by external stimuli. Here we report the first ever computational study of translational and rotational motion of self-propelled Janus tracers in a het- erogeneous polymeric environment. The presence of polymers makes the translational mean square displacement (MSD) of the Janus tracer to grow very slowly as compared to that of a free Janus tracer, but surprisingly the mean square angular displacement (MSAD) is significantly increased as observed in a recent experiment. Moreover, with the increasing propulsion velocity, MSAD grows even faster. However, when the repulsive polymers are replaced with polymers with sticky zones, MSD and MSAD both show sharp decline.

Text-to-image (T2I) generative diffusion models have demonstrated outstanding performance in synthesizing diverse, high-quality visuals from text captions. Several layout-to-image models have been developed to control the generation process by utilizing a wide range of layouts, such as segmentation maps, edges, and human keypoints. In this work, we propose ObjectDiffusion, a model that conditions T2I diffusion models on semantic and spatial grounding information, enabling the precise rendering and placement of desired objects in specific locations defined by bounding boxes. To achieve this, we make substantial modifications to the network architecture introduced in ControlNet to integrate it with the grounding method proposed in GLIGEN. We fine-tune ObjectDiffusion on the COCO2017 training dataset and evaluate it on the COCO2017 validation dataset. Our model improves the precision and quality of controllable image generation, achieving an AP_{50} of 46.6, an AR of 44.5, and an FID of 19.8, outperforming the current SOTA model trained on open-source datasets across all three metrics. ObjectDiffusion demonstrates a distinctive capability in synthesizing diverse, high-quality, high-fidelity images that seamlessly conform to the semantic and spatial control layout. Evaluated in qualitative and quantitative tests, ObjectDiffusion exhibits remarkable grounding capabilities in closed-set and open-set vocabulary settings across a wide variety of contexts. The qualitative assessment verifies the ability of ObjectDiffusion to generate multiple detailed objects in varying sizes, forms, and locations.

The recent wave of one-step generative models, which compress the multi-step trajectory of diffusion via either distillation or learned flow maps, has reached an inflection point where they can generate high-quality images. Here, we ask a natural question that follows from these advances: what happens to the denoising trajectory of multi-step diffusion when generation is compressed into a single forward pass? We offer an empirical observation we call depth as time: the denoising computation that multi-step diffusion performs across sampling steps appears to unfold across the depth of a single forward pass, and can be recovered by decoding intermediate layers with the model's own output head. Most interestingly, we show that this depthwise computation depends on the transport task a flow map is trained to solve. The most surprising case is MeanFlow, where probing shorter transport intervals reveals both denoising and renoising within a single network evaluation. In contrast, generators trained without a time-indexed transport task, such as drifting models, do not exhibit the same depthwise denoising. Consequently, we show that models that exhibit the depthwise denoising phenomenon are more compressible across the layerwise computation: a MeanFlow SiT-L/2 model can be compressed by 16.6times in parameters into a single time-conditioned block. We offer an explanation for this denoise-then-renoise behavior and show that, when we treat the layerwise computation explicitly as a flow, a single time-conditioned block can be trained to denoise across layers, compressing a MeanFlow SiT-L/2 model by 16.6times in parameters. Together, these results suggest that the temporal computation of diffusion is not eliminated by one-step generation, but reorganized across network depth.

Computational pathology models infer biologically and clinically meaningful outcomes from histology, but their predictions are shaped by complex, intertwined tissue signals whose roles are important to understand. Common pixel- and feature-space perturbations can produce implausible tissue, making model responses difficult to interpret. We introduce CPathOGen, a conditional latent-diffusion framework for generating paired H\&E counterfactuals with explicit controls over cellular spatial organization, nuclear morphology, and stain appearance. Cellular maps condition spatial structure through a spatial encoder, while a morphology/appearance vector modulates denoising through blockwise feature-wise linear modulation (FiLM). On held-out H\&E tiles, CPathOGen generates visually plausible tissue with improved distributional agreement after spatially guided selection, as reflected by lower Fréchet Inception Distance (FID) and Kernel Inception Distance (KID); generated cells track requested abundance and position, and measured morphology and color vary monotonically with their controls. We use these verified interventions to probe pathology encoders with endpoint heads, task-specific classifiers, and survival models. Responses are quantified using total variation distance and prediction-flip rate. We further introduce the Biology-Nuisance Sensitivity Ratio, a metric that contrasts model sensitivity to biologically motivated morphology and spatial factors with sensitivity to non-biological, stain-related nuisance variation. CPathOGen provides a practical, fidelity-audited framework for evaluating robustness and controlled feature sensitivity in computational pathology model. https://github.com/a12dongithub/PathOGen{GitHub} and https://huggingface.co/a12donhf/CPathOGen{Hugging~Face}.

Diffusion-based image generators can now produce high-quality and diverse samples, but their success has yet to fully translate to 3D generation: existing diffusion methods can either generate low-resolution but 3D consistent outputs, or detailed 2D views of 3D objects but with potential structural defects and lacking view consistency or realism. We present HoloFusion, a method that combines the best of these approaches to produce high-fidelity, plausible, and diverse 3D samples while learning from a collection of multi-view 2D images only. The method first generates coarse 3D samples using a variant of the recently proposed HoloDiffusion generator. Then, it independently renders and upsamples a large number of views of the coarse 3D model, super-resolves them to add detail, and distills those into a single, high-fidelity implicit 3D representation, which also ensures view consistency of the final renders. The super-resolution network is trained as an integral part of HoloFusion, end-to-end, and the final distillation uses a new sampling scheme to capture the space of super-resolved signals. We compare our method against existing baselines, including DreamFusion, Get3D, EG3D, and HoloDiffusion, and achieve, to the best of our knowledge, the most realistic results on the challenging CO3Dv2 dataset.

In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current methods, such as patchifying, expedite processes in UNet and Transformer architectures but at the expense of representational capacity. Addressing this, we introduce the Diffusion State Space Model (DiffuSSM), an architecture that supplants attention mechanisms with a more scalable state space model backbone. This approach effectively handles higher resolutions without resorting to global compression, thus preserving detailed image representation throughout the diffusion process. Our focus on FLOP-efficient architectures in diffusion training marks a significant step forward. Comprehensive evaluations on both ImageNet and LSUN datasets at two resolutions demonstrate that DiffuSSMs are on par or even outperform existing diffusion models with attention modules in FID and Inception Score metrics while significantly reducing total FLOP usage.

Cell migration in vivo is often guided by chemical signals. Such chemotaxis, such as performed by immune cells migrating to a wound site, is complicated by the complex geometry inside living tissues. In this study, we extend our theoretical model of branched-cell migration on a network by introducing chemokine sources to explore the cellular response. The model predicts a speed-accuracy tradeoff, whereby slow cells are significantly more accurate and able to follow efficiently a weak chemoattractant signal. We then compare the model's predictions with experimental observations of neutrophils migrating to the site of laser-inflicted wound in a zebrafish larva fin, and migrating in-vitro inside a regular lattice of pillars. We find that the model captures the details of the sub-cellular response to the chemokine gradient, as well as the large-scale migration response. This comparison suggests that the neutrophils behave as fast cells, compromising their chemotaxis accuracy, which explains the functionality of these immune cells.

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing acceleration sampling techniques, though seeking to expedite the process, inevitably sacrifice performance to some extent, resulting in over-blurry restored outcomes. To address this issue, this study proposes a novel and efficient diffusion model for IR that significantly reduces the required number of diffusion steps. Our method avoids the need for post-acceleration during inference, thereby avoiding the associated performance deterioration. Specifically, our proposed method establishes a Markov chain that facilitates the transitions between the high-quality and low-quality images by shifting their residuals, substantially improving the transition efficiency. A carefully formulated noise schedule is devised to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experimental evaluations demonstrate that the proposed method achieves superior or comparable performance to current state-of-the-art methods on three classical IR tasks, namely image super-resolution, image inpainting, and blind face restoration, \textbf{even only with four sampling steps}. Our code and model are publicly available at https://github.com/zsyOAOA/ResShift.

We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady state single site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the non-gradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

Estimating single-cell responses across various perturbations facilitates the identification of key genes and enhances drug screening, significantly boosting experimental efficiency. However, single-cell sequencing is a destructive process, making it impossible to capture the same cell's phenotype before and after perturbation. Consequently, data collected under perturbed and unperturbed conditions are inherently unpaired. Existing methods either attempt to forcibly pair unpaired data using random sampling, or neglect the inherent relationship between unperturbed and perturbed cells during the modeling. In this work, we propose a framework based on Dual Diffusion Implicit Bridges (DDIB) to learn the mapping between different data distributions, effectively addressing the challenge of unpaired data. We further interpret this framework as a form of data augmentation. We integrate gene regulatory network (GRN) information to propagate perturbation signals in a biologically meaningful way, and further incorporate a masking mechanism to predict silent genes, improving the quality of generated profiles. Moreover, gene expression under the same perturbation often varies significantly across cells, frequently exhibiting a bimodal distribution that reflects intrinsic heterogeneity. To capture this, we introduce a more suitable evaluation metric. We propose Unlasting, dual conditional diffusion models that overcome the problem of unpaired single-cell perturbation data and strengthen the model's insight into perturbations under the guidance of the GRN, with a dedicated mask model designed to improve generation quality by predicting silent genes. In addition, we introduce a biologically grounded evaluation metric that better reflects the inherent heterogeneity in single-cell responses.

Generating high-resolution images with generative models has recently been made widely accessible by leveraging diffusion models pre-trained on large-scale datasets. Various techniques, such as MultiDiffusion and SyncDiffusion, have further pushed image generation beyond training resolutions, i.e., from square images to panorama, by merging multiple overlapping diffusion paths or employing gradient descent to maintain perceptual coherence. However, these methods suffer from significant computational inefficiencies due to generating and averaging numerous predictions, which is required in practice to produce high-quality and seamless images. This work addresses this limitation and presents a novel approach that eliminates the need to generate and average numerous overlapping denoising predictions. Our method shifts non-overlapping denoising windows over time, ensuring that seams in one timestep are corrected in the next. This results in coherent, high-resolution images with fewer overall steps. We demonstrate the effectiveness of our approach through qualitative and quantitative evaluations, comparing it with MultiDiffusion, SyncDiffusion, and StitchDiffusion. Our method offers several key benefits, including improved computational efficiency and faster inference times while producing comparable or better image quality.

Video sequences often contain structured noise and background artifacts that obscure dynamic content, posing challenges for accurate analysis and restoration. Robust principal component methods address this by decomposing data into low-rank and sparse components. Still, the sparsity assumption often fails to capture the rich variability present in real video data. To overcome this limitation, a hybrid framework that integrates low-rank temporal modeling with diffusion posterior sampling is proposed. The proposed method, Nuclear Diffusion, is evaluated on a real-world medical imaging problem, namely cardiac ultrasound dehazing, and demonstrates improved dehazing performance compared to traditional RPCA concerning contrast enhancement (gCNR) and signal preservation (KS statistic). These results highlight the potential of combining model-based temporal models with deep generative priors for high-fidelity video restoration.

Nanostructured Si is the most promising high-capacity anode material to substantially increase the energy density of Li-ion batteries. Among the remaining challenges is its low rate capability as compared to conventional materials. To understand better what controls the diffusion of Li in the amorphous Li-Si alloy, we use a novel machine-learning potential trained on more than 40,000 ab-initio calculations and nanosecond-scale molecular dynamics simulations, to visualize for the first time the delithiation of entire LiSi nanoparticles. Our results show that the Si host is not static but undergoes a dynamic rearrangement from isolated atoms, to chains, and clusters, with the Li diffusion strongly governed by this Si rearrangement. We find that the Li diffusivity is highest when Si segregates into clusters, so that Li diffusion proceeds via hopping between the Si clusters. The average size of Si clusters and the concentration range over which Si clustering occurs can thus function as design criteria for the development of rate-improved anodes based on modified Si.

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we study theoretically the consequences of membrane responsiveness and feedback on the steady-state force--flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, c_0, the driving force, f, and the polymer volume fraction, phi. In our model, solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force--flux relations, j(f), which we quantify in terms of the system's differential permeability, P_sys^{Delta}mathrm{dj}/{df}. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force, and largely tunable by attractive versus repulsive solute--membrane interactions. Moreover, controlling the input, c_0 and f, can lead to steady-state bistability of phi and hysteresis in the force--flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

High-resolution brain imaging can now capture not just synapse locations but their molecular composition, with the cost of such mapping falling exponentially. Yet such ultrastructural data has so far told us little about local neuronal physiology - specifically, the parameters (e.g., synaptic efficacies, local conductances) that govern neural dynamics. We propose to translate molecularly annotated ultrastructure into physiology, introducing the concept of an ultrastructure-to-dynamics compiler: a learned mapping from molecularly annotated ultrastructure to simulator-ready, uncertainty-aware physiological parameters. The requirement is paired training data, with jointly acquired ultrastructure from imaging, and dynamical responses to perturbations from physiological experiments. With this data we can train models that predict local physiology directly from structure. Such a compiler would support biophysical simulations by turning anatomical maps into models of circuit dynamics, shifting structure-to-function from a descriptive program to a predictive one and opening routes to understanding neural computation and forecasting intervention effects.

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models and Score-based Generative Models, where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance on the E(3) group can keep the physical stability of the frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation.

While diffusion models excel at generating images with conventional dimensions, pushing them to synthesize ultra-high-resolution imagery at extreme aspect ratios (EAR) often triggers catastrophic structural failures, such as object repetition and spatial fragmentation. This limitation fundamentally stems from a lack of robust spatial priors, as static text-to-image models are primarily trained on image distributions with conventional dimensions. To overcome this bottleneck, we present ScrollScape, a novel framework that reformulates EAR image synthesis into a continuous video generation process through two core innovations. By mapping the spatial expansion of a massive canvas to the temporal evolution of video frames, ScrollScape leverages the inherent temporal consistency of video models as a powerful global constraint to ensure long-range structural integrity. Specifically, Scanning Positional Encoding (ScanPE) distributes global coordinates across frames to act as a flexible moving camera, while Scrolling Super-Resolution (ScrollSR) leverages video super-resolution priors to circumvent memory bottlenecks, efficiently scaling outputs to an unprecedented 32K resolution. Fine-tuned on a curated 3K multi-ratio image dataset, ScrollScape effectively aligns pre-trained video priors with the EAR generation task. Extensive evaluations demonstrate that it significantly outperforms existing image-diffusion baselines by eliminating severe localized artifacts. Consequently, our method overcomes inherent structural bottlenecks to ensure exceptional global coherence and visual fidelity across diverse domains at extreme scales.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

We show how to use low-quality, synthetic, and out-of-distribution images to improve the quality of a diffusion model. Typically, diffusion models are trained on curated datasets that emerge from highly filtered data pools from the Web and other sources. We show that there is immense value in the lower-quality images that are often discarded. We present Ambient Diffusion Omni, a simple, principled framework to train diffusion models that can extract signal from all available images during training. Our framework exploits two properties of natural images -- spectral power law decay and locality. We first validate our framework by successfully training diffusion models with images synthetically corrupted by Gaussian blur, JPEG compression, and motion blur. We then use our framework to achieve state-of-the-art ImageNet FID, and we show significant improvements in both image quality and diversity for text-to-image generative modeling. The core insight is that noise dampens the initial skew between the desired high-quality distribution and the mixed distribution we actually observe. We provide rigorous theoretical justification for our approach by analyzing the trade-off between learning from biased data versus limited unbiased data across diffusion times.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

Survival prediction using whole slide images (WSIs) can be formulated as a multiple instance learning (MIL) problem. However, existing MIL methods often fail to explicitly capture pathological heterogeneity within WSIs, both globally -- through long-tailed morphological distributions, and locally through -- tile-level prediction uncertainty. Optimal transport (OT) provides a principled way of modeling such heterogeneity by incorporating marginal distribution constraints. Building on this insight, we propose OTSurv, a novel MIL framework from an optimal transport perspective. Specifically, OTSurv formulates survival predictions as a heterogeneity-aware OT problem with two constraints: (1) global long-tail constraint that models prior morphological distributions to avert both mode collapse and excessive uniformity by regulating transport mass allocation, and (2) local uncertainty-aware constraint that prioritizes high-confidence patches while suppressing noise by progressively raising the total transport mass. We then recast the initial OT problem, augmented by these constraints, into an unbalanced OT formulation that can be solved with an efficient, hardware-friendly matrix scaling algorithm. Empirically, OTSurv sets new state-of-the-art results across six popular benchmarks, achieving an absolute 3.6% improvement in average C-index. In addition, OTSurv achieves statistical significance in log-rank tests and offers high interpretability, making it a powerful tool for survival prediction in digital pathology. Our codes are available at https://github.com/Y-Research-SBU/OTSurv.

Reinforcement learning with stochastic optimal control offers a promising framework for diffusion fine-tuning, where a pre-trained diffusion model is optimized to generate paths that lead to a reward-tilted distribution. While these approaches enable optimization without access to explicit samples from the optimal distribution, they require training on rollouts under the current fine-tuned model, making them susceptible to reinforcing sub-optimal trajectories that yield poor rewards. To overcome this challenge, we introduce TRee Search Guided TRajectory-Aware Fine-Tuning for Discrete Diffusion (TR2-D2), a novel framework that optimizes reward-guided discrete diffusion trajectories with tree search to construct replay buffers for trajectory-aware fine-tuning. These buffers are generated using Monte Carlo Tree Search (MCTS) and subsequently used to fine-tune a pre-trained discrete diffusion model under a stochastic optimal control objective. We validate our framework on single- and multi-objective fine-tuning of biological sequence diffusion models, highlighting the overall effectiveness of TR2-D2 for reliable reward-guided fine-tuning in discrete sequence generation.

Peptide therapeutics, a major class of medicines, have achieved remarkable success across diseases such as diabetes and cancer, with landmark examples such as GLP-1 receptor agonists revolutionizing the treatment of type-2 diabetes and obesity. Despite their success, designing peptides that satisfy multiple conflicting objectives, such as target binding affinity, solubility, and membrane permeability, remains a major challenge. Classical drug development and structure-based design are ineffective for such tasks, as they fail to optimize global functional properties critical for therapeutic efficacy. Existing generative frameworks are largely limited to continuous spaces, unconditioned outputs, or single-objective guidance, making them unsuitable for discrete sequence optimization across multiple properties. To address this, we present PepTune, a multi-objective discrete diffusion model for the simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with state-dependent masking schedules and penalty-based objectives. To guide the diffusion process, we propose a Monte Carlo Tree Search (MCTS)-based strategy that balances exploration and exploitation to iteratively refine Pareto-optimal sequences. MCTS integrates classifier-based rewards with search-tree expansion, overcoming gradient estimation challenges and data sparsity inherent to discrete spaces. Using PepTune, we generate diverse, chemically-modified peptides optimized for multiple therapeutic properties, including target binding affinity, membrane permeability, solubility, hemolysis, and non-fouling characteristics on various disease-relevant targets. In total, our results demonstrate that MCTS-guided discrete diffusion is a powerful and modular approach for multi-objective sequence design in discrete state spaces.

We present a set of numerical simulations of the dynamical evolution of compact planetary systems migrating in a protoplanetary disk whose inner edge is sculpted by the interaction with the stellar magnetic field, as described in Yu et al. (2023). We demonstrate that the resulting final distribution of neighbouring planet period ratios contains only a small surviving fraction of resonant systems, in accordance with observations. The resulting planetary architectures are largely in place by the end of the protoplanetary disk phase (within a few Myr), and do not require significant later dynamical evolution. The divergence of planetary pairs during gas disk dispersal also leads to the excitation of eccentricities when pairs cross mean motion resonances in a divergent fashion. The resulting distribution of remnant free eccentricities is consistent with the values inferred from the observation of transit durations and transit timing variations. We furthermore demonstrate that this conclusion is not significantly altered by tides, assuming standard values for tidal dissipation in Earth or Neptune-class planets. These results demonstrate that the observed spacing and residual dynamical excitation of compact planetary systems can be reproduced by migration through a protoplanetary disk, as long as the inner disk boundary is modelled as a gradual rollover, instead of a sharp transition. Such an effect can be achieved when the model accounts for the diffusion of the stellar magnetic field into the disk. The resulting divergence of planetary pairs during the magnetospheric rebound phase breaks the resonant chains, resulting in a better match to observations than disk models with more traditional inner boundaries.

Molecular communication (MC) engineering is inspired by the use of chemical signals as information carriers in cell biology. The biological nature of chemical signaling makes MC a promising methodology for interdisciplinary applications requiring communication between cells and other microscale devices. However, since the life sciences and communications engineering fields have distinct approaches to formulating and solving research problems, the mismatch between them can hinder the translation of research results and impede the development and implementation of interdisciplinary solutions. To bridge this gap, this survey proposes a novel communication hierarchy for MC signaling in cell biology and maps phenomena, contributions, and problems to the hierarchy. The hierarchy includes: 1) the Physical Signal Propagation level; 2) the Physical and Chemical Signal Interaction level; 3) the Signal-Data Interface level; 4) the Local Data Abstraction level; and 5) the Application level. To further demonstrate the proposed hierarchy, it is applied to case studies on quorum sensing, neuronal signaling, and communication via DNA. Finally, several open problems are identified for each level and the integration of multiple levels. The proposed hierarchy provides language for communication engineers to study and interface with biological systems, and also helps biologists to understand how communications engineering concepts can be exploited to interpret, control, and manipulate signaling in cell biology.

This paper presents a comprehensive study on the unified module for accelerating stable-diffusion processes, specifically focusing on the lcm-lora module. Stable-diffusion processes play a crucial role in various scientific and engineering domains, and their acceleration is of paramount importance for efficient computational performance. The standard iterative procedures for solving fixed-source discrete ordinates problems often exhibit slow convergence, particularly in optically thick scenarios. To address this challenge, unconditionally stable diffusion-acceleration methods have been developed, aiming to enhance the computational efficiency of transport equations and discrete ordinates problems. This study delves into the theoretical foundations and numerical results of unconditionally stable diffusion synthetic acceleration methods, providing insights into their stability and performance for model discrete ordinates problems. Furthermore, the paper explores recent advancements in diffusion model acceleration, including on device acceleration of large diffusion models via gpu aware optimizations, highlighting the potential for significantly improved inference latency. The results and analyses in this study provide important insights into stable diffusion processes and have important ramifications for the creation and application of acceleration methods specifically, the lcm-lora module in a variety of computing environments.

Recent surge in large-scale generative models has spurred the development of vast fields in computer vision. In particular, text-to-image diffusion models have garnered widespread adoption across diverse domain due to their potential for high-fidelity image generation. Nonetheless, existing large-scale diffusion models are confined to generate images of up to 1K resolution, which is far from meeting the demands of contemporary commercial applications. Directly sampling higher-resolution images often yields results marred by artifacts such as object repetition and distorted shapes. Addressing the aforementioned issues typically necessitates training or fine-tuning models on higher resolution datasets. However, this undertaking poses a formidable challenge due to the difficulty in collecting large-scale high-resolution contents and substantial computational resources. While several preceding works have proposed alternatives, they often fail to produce convincing results. In this work, we probe the generative ability of diffusion models at higher resolution beyond its original capability and propose a novel progressive approach that fully utilizes generated low-resolution image to guide the generation of higher resolution image. Our method obviates the need for additional training or fine-tuning which significantly lowers the burden of computational costs. Extensive experiments and results validate the efficiency and efficacy of our method. Project page: https://yhyun225.github.io/DiffuseHigh/

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based models exhibit great potential in generating high-quality images for super-resolution tasks. However, existing models encounter difficulties in directly predicting high-frequency information of wide bandwidth by solely utilizing the high-resolution ground truth as the target for all sampling timesteps. To tackle this problem and achieve higher-quality super-resolution, we propose a novel Frequency Domain-guided multiscale Diffusion model (FDDiff), which decomposes the high-frequency information complementing process into finer-grained steps. In particular, a wavelet packet-based frequency complement chain is developed to provide multiscale intermediate targets with increasing bandwidth for reverse diffusion process. Then FDDiff guides reverse diffusion process to progressively complement the missing high-frequency details over timesteps. Moreover, we design a multiscale frequency refinement network to predict the required high-frequency components at multiple scales within one unified network. Comprehensive evaluations on popular benchmarks are conducted, and demonstrate that FDDiff outperforms prior generative methods with higher-fidelity super-resolution results.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.