Daily Papers

Biomolecular interactions underpin almost all biological processes, and their rational design is central to programming new biological functions. Generative AI models have emerged as powerful tools for molecular design, yet most remain specialized for individual molecular types and lack fine-grained control over interaction details. Here we present ODesign, an all-atom generative world model for all-to-all biomolecular interaction design. ODesign allows scientists to specify epitopes on arbitrary targets and generate diverse classes of binding partners with fine-grained control. Across entity-, token-, and atom-level benchmarks in the protein modality, ODesign demonstrates superior controllability and performance to modality-specific baselines. Extending beyond proteins, it generalizes to nucleic acid and small-molecule design, enabling interaction types such as protein-binding RNA/DNA and RNA/DNA-binding ligands that were previously inaccessible. By unifying multimodal biomolecular interactions within a single generative framework, ODesign moves toward a general-purpose molecular world model capable of programmable design. ODesign is available at https://odesign.lglab.ac.cn ,

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time-series naturally and incorporate knowledge of physical systems into deep learning models. However, the practical applications of Neural ODEs are limited due to long inference times, because the outputs of the embedded ODE layers are computed numerically with differential equation solvers that can be computationally demanding. Here we show that mathematical model order reduction methods can be used for compressing and accelerating Neural ODEs by accurately simulating the continuous nonlinear dynamics in low-dimensional subspaces. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and interpolation operations as layers of the neural network. We validate our approach by comparing it to neuron pruning and SVD-based weight truncation methods from the literature in image and time-series classification tasks. The methods are evaluated by acceleration versus accuracy when adjusting the level of compression. On this spectrum, we achieve a favourable balance over existing methods by using model order reduction when compressing a convolutional Neural ODE. In compressing a recurrent Neural ODE, SVD-based weight truncation yields good performance. Based on our results, our integration of model order reduction with Neural ODEs can facilitate efficient, dynamical system-driven deep learning in resource-constrained applications.

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.

To accelerate diffusion model inference, numerical solvers perform poorly at extremely small steps, while distillation techniques often introduce complexity and instability. This work presents an intermediate strategy, balancing performance and cost, by learning ODE integration using loss functions derived from the derivative-integral relationship, inspired by Monte Carlo integration and Picard iteration. From a geometric perspective, the losses operate by gradually extending the tangent to the secant, thus are named as secant losses. The target of secant losses is the same as that of diffusion models, or the diffusion model itself, leading to great training stability. By fine-tuning or distillation, the secant version of EDM achieves a 10-step FID of 2.14 on CIFAR-10, while the secant version of SiT-XL/2 attains a 4-step FID of 2.27 and an 8-step FID of 1.96 on ImageNet-256times256. Code is available at https://github.com/poppuppy/secant-expectation.

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.

While diffusion models achieve state-of-the-art generation quality, they still suffer from computationally expensive sampling. Recent works address this issue with gradient-based optimization methods that distill a few-step ODE diffusion solver from the full sampling process, reducing the number of function evaluations from dozens to just a few. However, these approaches often rely on intricate training techniques and do not explicitly focus on preserving fine-grained details. In this paper, we introduce the Generalized Solver: a simple parameterization of the ODE sampler that does not require additional training tricks and improves quality over existing approaches. We further combine the original distillation loss with adversarial training, which mitigates artifacts and enhances detail fidelity. We call the resulting method the Generalized Adversarial Solver and demonstrate its superior performance compared to existing solver training methods under similar resource constraints. Code is available at https://github.com/3145tttt/GAS.

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function evaluations (NFEs) to transform Gaussian noise samples into images, resulting in higher computational costs compared to single-step generative models such as GANs or VAEs. Therefore, reducing the number of NFEs while preserving generation quality is crucial. To address this, we propose LD3, a lightweight framework designed to learn the optimal time discretization for sampling. LD3 can be combined with various samplers and consistently improves generation quality without having to retrain resource-intensive neural networks. We demonstrate analytically and empirically that LD3 improves sampling efficiency with much less computational overhead. We evaluate our method with extensive experiments on 7 pre-trained models, covering unconditional and conditional sampling in both pixel-space and latent-space DPMs. We achieve FIDs of 2.38 (10 NFE), and 2.27 (10 NFE) on unconditional CIFAR10 and AFHQv2 in 5-10 minutes of training. LD3 offers an efficient approach to sampling from pre-trained diffusion models. Code is available at https://github.com/vinhsuhi/LD3.

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and employed in practice, the theoretical understandings about convergence properties of the probability flow ODE are still quite limited. In this paper, we provide the first non-asymptotic convergence analysis for a general class of probability flow ODE samplers in 2-Wasserstein distance, assuming accurate score estimates. We then consider various examples and establish results on the iteration complexity of the corresponding ODE-based samplers.

Antibodies are Y-shaped proteins that neutralize pathogens and constitute the core of our adaptive immune system. De novo generation of new antibodies that target specific antigens holds the key to accelerating vaccine discovery. However, this co-design of the amino acid sequence and the 3D structure subsumes and accentuates some central challenges from multiple tasks, including protein folding (sequence to structure), inverse folding (structure to sequence), and docking (binding). We strive to surmount these challenges with a new generative model AbODE that extends graph PDEs to accommodate both contextual information and external interactions. Unlike existing approaches, AbODE uses a single round of full-shot decoding and elicits continuous differential attention that encapsulates and evolves with latent interactions within the antibody as well as those involving the antigen. We unravel fundamental connections between AbODE and temporal networks as well as graph-matching networks. The proposed model significantly outperforms existing methods on standard metrics across benchmarks.

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

Real-world text applications often involve composing a wide range of text control operations, such as editing the text w.r.t. an attribute, manipulating keywords and structure, and generating new text of desired properties. Prior work typically learns/finetunes a language model (LM) to perform individual or specific subsets of operations. Recent research has studied combining operations in a plug-and-play manner, often with costly search or optimization in the complex sequence space. This paper proposes a new efficient approach for composable text operations in the compact latent space of text. The low-dimensionality and differentiability of the text latent vector allow us to develop an efficient sampler based on ordinary differential equations (ODEs) given arbitrary plug-in operators (e.g., attribute classifiers). By connecting pretrained LMs (e.g., GPT2) to the latent space through efficient adaption, we then decode the sampled vectors into desired text sequences. The flexible approach permits diverse control operators (sentiment, tense, formality, keywords, etc.) acquired using any relevant data from different domains. Experiments show that composing those operators within our approach manages to generate or edit high-quality text, substantially improving over previous methods in terms of generation quality and efficiency.

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational expense challenging to predict. In this manuscript, we increase the "implicitness" of the DEQ by redefining the method in terms of an infinite time neural ODE, which paradoxically decreases the training cost over a standard neural ODE by 2-4x. Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer? To solve this, we develop Skip and Skip Reg. DEQ, an implicit-explicit (IMEX) layer that simultaneously trains an explicit prediction followed by an implicit correction. We show that training this explicit predictor is free and even decreases the training time by 1.11-3.19x. Together, this manuscript shows how bridging the dichotomy of implicit and explicit deep learning can combine the advantages of both techniques.

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous models still lacks a solid mathematical foundation. In this article, we take a step in this direction by establishing an implicit regularization of deep residual networks towards neural ODEs, for nonlinear networks trained with gradient flow. We prove that if the network is initialized as a discretization of a neural ODE, then such a discretization holds throughout training. Our results are valid for a finite training time, and also as the training time tends to infinity provided that the network satisfies a Polyak-Lojasiewicz condition. Importantly, this condition holds for a family of residual networks where the residuals are two-layer perceptrons with an overparameterization in width that is only linear, and implies the convergence of gradient flow to a global minimum. Numerical experiments illustrate our results.

Deep Equilibrium Models (DEQs) and Neural Ordinary Differential Equations (Neural ODEs) are two branches of implicit models that have achieved remarkable success owing to their superior performance and low memory consumption. While both are implicit models, DEQs and Neural ODEs are derived from different mathematical formulations. Inspired by homotopy continuation, we establish a connection between these two models and illustrate that they are actually two sides of the same coin. Homotopy continuation is a classical method of solving nonlinear equations based on a corresponding ODE. Given this connection, we proposed a new implicit model called HomoODE that inherits the property of high accuracy from DEQs and the property of stability from Neural ODEs. Unlike DEQs, which explicitly solve an equilibrium-point-finding problem via Newton's methods in the forward pass, HomoODE solves the equilibrium-point-finding problem implicitly using a modified Neural ODE via homotopy continuation. Further, we developed an acceleration method for HomoODE with a shared learnable initial point. It is worth noting that our model also provides a better understanding of why Augmented Neural ODEs work as long as the augmented part is regarded as the equilibrium point to find. Comprehensive experiments with several image classification tasks demonstrate that HomoODE surpasses existing implicit models in terms of both accuracy and memory consumption.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

Benefiting from language flexibility and compositionality, humans naturally intend to use language to command an embodied agent for complex tasks such as navigation and object manipulation. In this work, we aim to fill the blank of the last mile of embodied agents -- object manipulation by following human guidance, e.g., "move the red mug next to the box while keeping it upright." To this end, we introduce an Automatic Manipulation Solver (AMSolver) system and build a Vision-and-Language Manipulation benchmark (VLMbench) based on it, containing various language instructions on categorized robotic manipulation tasks. Specifically, modular rule-based task templates are created to automatically generate robot demonstrations with language instructions, consisting of diverse object shapes and appearances, action types, and motion constraints. We also develop a keypoint-based model 6D-CLIPort to deal with multi-view observations and language input and output a sequence of 6 degrees of freedom (DoF) actions. We hope the new simulator and benchmark will facilitate future research on language-guided robotic manipulation.

We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the probabilistic factors of a graphical model. In this work, we replace each crafted factor with a differentiable neural network enabling the factors to be learned using an efficient optimization routine from labeled data. By combining differentiable neural networks with an efficient belief propagation algorithm, our method learns to maintain a set of marginal posterior samples using end-to-end training. We evaluate our differentiable nonparametric belief propagation (DNBP) method on a set of articulated pose tracking tasks and compare performance with learned baselines. Results from these experiments demonstrate the effectiveness of using learned factors for tracking and suggest the practical advantage over hand-crafted approaches. The project webpage is available at: https://progress.eecs.umich.edu/projects/dnbp/ .