Daily Papers

This paper is about the problem of learning a stochastic policy for generating an object (like a molecular graph) from a sequence of actions, such that the probability of generating an object is proportional to a given positive reward for that object. Whereas standard return maximization tends to converge to a single return-maximizing sequence, there are cases where we would like to sample a diverse set of high-return solutions. These arise, for example, in black-box function optimization when few rounds are possible, each with large batches of queries, where the batches should be diverse, e.g., in the design of new molecules. One can also see this as a problem of approximately converting an energy function to a generative distribution. While MCMC methods can achieve that, they are expensive and generally only perform local exploration. Instead, training a generative policy amortizes the cost of search during training and yields to fast generation. Using insights from Temporal Difference learning, we propose GFlowNet, based on a view of the generative process as a flow network, making it possible to handle the tricky case where different trajectories can yield the same final state, e.g., there are many ways to sequentially add atoms to generate some molecular graph. We cast the set of trajectories as a flow and convert the flow consistency equations into a learning objective, akin to the casting of the Bellman equations into Temporal Difference methods. We prove that any global minimum of the proposed objectives yields a policy which samples from the desired distribution, and demonstrate the improved performance and diversity of GFlowNet on a simple domain where there are many modes to the reward function, and on a molecule synthesis task.

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

Scene flow estimation determines a scene's 3D motion field, by predicting the motion of points in the scene, especially for aiding tasks in autonomous driving. Many networks with large-scale point clouds as input use voxelization to create a pseudo-image for real-time running. However, the voxelization process often results in the loss of point-specific features. This gives rise to a challenge in recovering those features for scene flow tasks. Our paper introduces DeFlow which enables a transition from voxel-based features to point features using Gated Recurrent Unit (GRU) refinement. To further enhance scene flow estimation performance, we formulate a novel loss function that accounts for the data imbalance between static and dynamic points. Evaluations on the Argoverse 2 scene flow task reveal that DeFlow achieves state-of-the-art results on large-scale point cloud data, demonstrating that our network has better performance and efficiency compared to others. The code is open-sourced at https://github.com/KTH-RPL/deflow.

Graph generation aims to sample discrete node and edge attributes while satisfying coupled structural constraints. Diffusion models for graphs often adopt largely factorized forward-noising, and many flow-matching methods start from factorized reference noise and coordinate-wise interpolation, so node-edge coupling is not encoded by the generative geometry and must be recovered implicitly by the core network, which can be brittle after discrete decoding. Bayesian Flow Networks (BFNs) evolve distribution parameters and naturally support discrete generation. But classical BFNs typically rely on factorized beliefs and independent channels, which limit geometric evidence fusion. We propose Variational Bayesian Flow Network (VBFN), which performs a variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions. Each Bayesian update reduces to solving a symmetric positive definite linear system, enabling coupled node and edge updates within a single fusion step. We construct sample-agnostic sparse precisions from a representation-induced dependency graph, thereby avoiding label leakage while enforcing node-edge consistency. On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.

Despite the success of Large-Vision Language Models (LVLMs), general optimization objectives (e.g., standard MLE) fail to constrain visual trajectories, leading to language bias and hallucination. To mitigate this, current methods introduce geometric priors from visual experts as additional supervision. However, we observe that such supervision is typically suboptimal: it is biased toward geometric precision and offers limited reasoning utility. To bridge this gap, we propose Perceptual Flow Network (PFlowNet), which eschews rigid alignment with the expert priors and achieves interpretable yet more effective visual reasoning. Specifically, PFlowNet decouples perception from reasoning to establish a self-conditioned generation process. Based on this, it integrates multi-dimensional rewards with vicinal geometric shaping via variational reinforcement learning, thereby facilitating reasoning-oriented perceptual behaviors while preserving visual reliability. PFlowNet delivers a provable performance guarantee and competitive empirical results, particularly setting new SOTA records on V* Bench (90.6%) and MME-RealWorld-lite (67.0%).

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that they are restricted to discrete spaces. We present a theory for generalized GFlowNets, which encompasses both existing discrete GFlowNets and ones with continuous or hybrid state spaces, and perform experiments with two goals in mind. First, we illustrate critical points of the theory and the importance of various assumptions. Second, we empirically demonstrate how observations about discrete GFlowNets transfer to the continuous case and show strong results compared to non-GFlowNet baselines on several previously studied tasks. This work greatly widens the perspectives for the application of GFlowNets in probabilistic inference and various modeling settings.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

Generative flow networks (GFlowNets) are sequential sampling models trained to match a given distribution. GFlowNets have been successfully applied to various structured object generation tasks, sampling a diverse set of high-reward objects quickly. We propose expected flow networks (EFlowNets), which extend GFlowNets to stochastic environments. We show that EFlowNets outperform other GFlowNet formulations in stochastic tasks such as protein design. We then extend the concept of EFlowNets to adversarial environments, proposing adversarial flow networks (AFlowNets) for two-player zero-sum games. We show that AFlowNets learn to find above 80% of optimal moves in Connect-4 via self-play and outperform AlphaZero in tournaments.

Generative Flow Networks (GFlowNets) are amortized samplers that learn stochastic policies to sequentially generate compositional objects from a given unnormalized reward distribution. They can generate diverse sets of high-reward objects, which is an important consideration in scientific discovery tasks. However, as they are typically trained from a given extrinsic reward function, it remains an important open challenge about how to leverage the power of pre-training and train GFlowNets in an unsupervised fashion for efficient adaptation to downstream tasks. Inspired by recent successes of unsupervised pre-training in various domains, we introduce a novel approach for reward-free pre-training of GFlowNets. By framing the training as a self-supervised problem, we propose an outcome-conditioned GFlowNet (OC-GFN) that learns to explore the candidate space. Specifically, OC-GFN learns to reach any targeted outcomes, akin to goal-conditioned policies in reinforcement learning. We show that the pre-trained OC-GFN model can allow for a direct extraction of a policy capable of sampling from any new reward functions in downstream tasks. Nonetheless, adapting OC-GFN on a downstream task-specific reward involves an intractable marginalization over possible outcomes. We propose a novel way to approximate this marginalization by learning an amortized predictor enabling efficient fine-tuning. Extensive experimental results validate the efficacy of our approach, demonstrating the effectiveness of pre-training the OC-GFN, and its ability to swiftly adapt to downstream tasks and discover modes more efficiently. This work may serve as a foundation for further exploration of pre-training strategies in the context of GFlowNets.

Generative Flow Networks (GFlowNets) have recently emerged as a suitable framework for generating diverse and high-quality molecular structures by learning from rewards treated as unnormalized distributions. Previous works in this framework often restrict exploration by using predefined molecular fragments as building blocks, limiting the chemical space that can be accessed. In this work, we introduce Atomic GFlowNets (A-GFNs), a foundational generative model leveraging individual atoms as building blocks to explore drug-like chemical space more comprehensively. We propose an unsupervised pre-training approach using drug-like molecule datasets, which teaches A-GFNs about inexpensive yet informative molecular descriptors such as drug-likeliness, topological polar surface area, and synthetic accessibility scores. These properties serve as proxy rewards, guiding A-GFNs towards regions of chemical space that exhibit desirable pharmacological properties. We further implement a goal-conditioned finetuning process, which adapts A-GFNs to optimize for specific target properties. In this work, we pretrain A-GFN on a subset of ZINC dataset, and by employing robust evaluation metrics we show the effectiveness of our approach when compared to other relevant baseline methods for a wide range of drug design tasks. The code is accessible at https://github.com/diamondspark/AGFN.

The task of human reposing involves generating a realistic image of a person standing in an arbitrary conceivable pose. There are multiple difficulties in generating perceptually accurate images, and existing methods suffer from limitations in preserving texture, maintaining pattern coherence, respecting cloth boundaries, handling occlusions, manipulating skin generation, etc. These difficulties are further exacerbated by the fact that the possible space of pose orientation for humans is large and variable, the nature of clothing items is highly non-rigid, and the diversity in body shape differs largely among the population. To alleviate these difficulties and synthesize perceptually accurate images, we propose VGFlow. Our model uses a visibility-guided flow module to disentangle the flow into visible and invisible parts of the target for simultaneous texture preservation and style manipulation. Furthermore, to tackle distinct body shapes and avoid network artifacts, we also incorporate a self-supervised patch-wise "realness" loss to improve the output. VGFlow achieves state-of-the-art results as observed qualitatively and quantitatively on different image quality metrics (SSIM, LPIPS, FID).

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods. Our code is available at https://github.com/zmy1116/phylogfn.

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."

In this work, we introduce ChemBFN, a language model that handles chemistry tasks based on Bayesian flow networks working on discrete data. A new accuracy schedule is proposed to improve the sampling quality by significantly reducing the reconstruction loss. We show evidence that our method is appropriate for generating molecules with satisfied diversity even when a smaller number of sampling steps is used. A classifier-free guidance method is adapted for conditional generation. It is also worthwhile to point out that after generative training, our model can be fine-tuned on regression and classification tasks with the state-of-the-art performance, which opens the gate of building all-in-one models in a single module style. Our model has been open sourced at https://github.com/Augus1999/bayesian-flow-network-for-chemistry.

We introduce UNITY, a Universal-to-Specialized adapter for efficient and scalable composite conditioning in diffusion based image generation. Unlike prior methods that train separate adapters for each conditioning modality, UNITY jointly learns shared semantics across multiple conditioning types and subsequently specializes without modifying the underlying architecture. The proposed two stage training paradigm consists of a Universal Stage that captures cross modal representations across all conditioning modalities using half of the total training steps, followed by a Specialization Stage that refines modality specific features using the remaining training budget. At the core of UNITY are the Morphable Attention Flow (MAF) Network and Morph Wrapper modules, which enable channel aware and spatially adaptive feature alignment through learnable flow fields and attention based fusion. This constant complexity formulation supports flexible operation under both single and composite conditioning settings while significantly reducing inference latency and memory consumption. Extensive experiments across multiple datasets demonstrate that UNITY achieves state of the art image fidelity while maintaining superior memory efficiency. Code: https://github.com/arya-domain/UNITY

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is challenging and requires restrictive approximations. Monte Carlo Dropout has been widely used as a relatively cheap way for approximate Inference and to estimate uncertainty with deep neural networks. Traditionally, the dropout mask is sampled independently from a fixed distribution. Recent works show that the dropout mask can be viewed as a latent variable, which can be inferred with variational inference. These methods face two important challenges: (a) the posterior distribution over masks can be highly multi-modal which can be difficult to approximate with standard variational inference and (b) it is not trivial to fully utilize sample-dependent information and correlation among dropout masks to improve posterior estimation. In this work, we propose GFlowOut to address these issues. GFlowOut leverages the recently proposed probabilistic framework of Generative Flow Networks (GFlowNets) to learn the posterior distribution over dropout masks. We empirically demonstrate that GFlowOut results in predictive distributions that generalize better to out-of-distribution data, and provide uncertainty estimates which lead to better performance in downstream tasks.

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the multi-modality and noise-sensitive nature of molecule geometry. This work introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits molecule geometry by modeling diverse modalities in the differentiable parameter space of distributions. GeoBFN maintains the SE-(3) invariant density modeling property by incorporating equivariant inter-dependency modeling on parameters of distributions and unifying the probabilistic modeling of different modalities. Through optimized training and sampling techniques, we demonstrate that GeoBFN achieves state-of-the-art performance on multiple 3D molecule generation benchmarks in terms of generation quality (90.87% molecule stability in QM9 and 85.6% atom stability in GEOM-DRUG. GeoBFN can also conduct sampling with any number of steps to reach an optimal trade-off between efficiency and quality (e.g., 20-times speedup without sacrificing performance).

Feature interaction has long been a cornerstone of ranking models in large-scale recommender systems due to its proven effectiveness in capturing complex dependencies among features. However, existing feature interaction strategies face two critical challenges in industrial applications: (1) The vast number of categorical and sequential features makes exhaustive interaction computationally prohibitive, often resulting in optimization difficulties. (2) Real-world recommender systems typically involve multiple prediction objectives, yet most current approaches apply feature interaction modules prior to the multi-task learning layers. This late-fusion design overlooks task-specific feature dependencies and inherently limits the capacity of multi-task modeling. To address these limitations, we propose the Information Flow Network (INFNet), a task-aware architecture designed for large-scale recommendation scenarios. INFNet distinguishes features into three token types, categorical tokens, sequence tokens, and task tokens, and introduces a novel dual-flow design comprising heterogeneous and homogeneous alternating information blocks. For heterogeneous information flow, we employ a cross-attention mechanism with proxy that facilitates efficient cross-modal token interaction with balanced computational cost. For homogeneous flow, we design type-specific Proxy Gated Units (PGUs) to enable fine-grained intra-type feature processing. Extensive experiments on multiple offline benchmarks confirm that INFNet achieves state-of-the-art performance. Moreover, INFNet has been successfully deployed in a commercial online advertising system, yielding significant gains of +1.587% in Revenue (REV) and +1.155% in Click-Through Rate (CTR).

In this paper, we present gfnx, a fast and scalable package for training and evaluating Generative Flow Networks (GFlowNets) written in JAX. gfnx provides an extensive set of environments and metrics for benchmarking, accompanied with single-file implementations of core objectives for training GFlowNets. We include synthetic hypergrids, multiple sequence generation environments with various editing regimes and particular reward designs for molecular generation, phylogenetic tree construction, Bayesian structure learning, and sampling from the Ising model energy. Across different tasks, gfnx achieves significant wall-clock speedups compared to Pytorch-based benchmarks (such as torchgfn library) and author implementations. For example, gfnx achieves up to 55 times speedup on CPU-based sequence generation environments, and up to 80 times speedup with the GPU-based Bayesian network structure learning setup. Our package provides a diverse set of benchmarks and aims to standardize empirical evaluation and accelerate research and applications of GFlowNets. The library is available on GitHub (https://github.com/d-tiapkin/gfnx) and on pypi (https://pypi.org/project/gfnx/). Documentation is available on https://gfnx.readthedocs.io.

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates X and response y. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.

Vision-Language Models (VLMs) have recently shown promising advancements in sequential decision-making tasks through task-specific fine-tuning. However, common fine-tuning methods, such as Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) techniques like Proximal Policy Optimization (PPO), present notable limitations: SFT assumes Independent and Identically Distributed (IID) data, while PPO focuses on maximizing cumulative rewards. These limitations often restrict solution diversity and hinder generalization in multi-step reasoning tasks. To address these challenges, we introduce a novel framework, GFlowVLM, a framework that fine-tune VLMs using Generative Flow Networks (GFlowNets) to promote generation of diverse solutions for complex reasoning tasks. GFlowVLM models the environment as a non-Markovian decision process, allowing it to capture long-term dependencies essential for real-world applications. It takes observations and task descriptions as inputs to prompt chain-of-thought (CoT) reasoning which subsequently guides action selection. We use task based rewards to fine-tune VLM with GFlowNets. This approach enables VLMs to outperform prior fine-tuning methods, including SFT and RL. Empirical results demonstrate the effectiveness of GFlowVLM on complex tasks such as card games (NumberLine, BlackJack) and embodied planning tasks (ALFWorld), showing enhanced training efficiency, solution diversity, and stronger generalization capabilities across both in-distribution and out-of-distribution scenarios.

Structure-Based molecule optimization (SBMO) aims to optimize molecules with both continuous coordinates and discrete types against protein targets. A promising direction is to exert gradient guidance on generative models given its remarkable success in images, but it is challenging to guide discrete data and risks inconsistencies between modalities. To this end, we leverage a continuous and differentiable space derived through Bayesian inference, presenting Molecule Joint Optimization (MolJO), the gradient-based SBMO framework that facilitates joint guidance signals across different modalities while preserving SE(3)-equivariance. We introduce a novel backward correction strategy that optimizes within a sliding window of the past histories, allowing for a seamless trade-off between explore-and-exploit during optimization. MolJO achieves state-of-the-art performance on CrossDocked2020 benchmark (Success Rate 51.3%, Vina Dock -9.05 and SA 0.78), more than 4x improvement in Success Rate compared to the gradient-based counterpart, and 2x "Me-Better" Ratio as much as 3D baselines. Furthermore, we extend MolJO to a wide range of optimization settings, including multi-objective optimization and challenging tasks in drug design such as R-group optimization and scaffold hopping, further underscoring its versatility. Code is available at https://github.com/AlgoMole/MolCRAFT.

Generating novel molecules with higher properties than the training space, namely the out-of-distribution generation, is important for {de~novo} drug design. However, it is not easy for distribution learning-based models, for example diffusion models, to solve this challenge as these methods are designed to fit the distribution of training data as close as possible. In this paper, we show that Bayesian flow network is capable of effortlessly generating high quality out-of-distribution samples that meet several scenarios. We introduce a semi-autoregressive training/sampling method that helps to enhance the model performance and surpass the state-of-the-art models.

While large language models (LLMs) are increasingly adapted for recommendation systems via supervised fine-tuning (SFT), this approach amplifies popularity bias due to its likelihood maximization objective, compromising recommendation diversity and fairness. To address this, we present Flow-guided fine-tuning recommender (Flower), which replaces SFT with a Generative Flow Network (GFlowNet) framework that enacts process supervision through token-level reward propagation. Flower's key innovation lies in decomposing item-level rewards into constituent token rewards, enabling direct alignment between token generation probabilities and their reward signals. This mechanism achieves three critical advancements: (1) popularity bias mitigation and fairness enhancement through empirical distribution matching, (2) preservation of diversity through GFlowNet's proportional sampling, and (3) flexible integration of personalized preferences via adaptable token rewards. Experiments demonstrate Flower's superior distribution-fitting capability and its significant advantages over traditional SFT in terms of fairness, diversity, and accuracy, highlighting its potential to improve LLM-based recommendation systems. The implementation is available via https://github.com/Mr-Peach0301/Flower

RNA function arises from the coupling of nucleotide sequence and three-dimensional structure, motivating their joint design. Coordinating global folding with nucleotide-level detail remains challenging under limited structural supervision. We introduce La-Ribo, a generative framework for RNA sequence-structure co-design via geometry-latent flow matching. La-Ribo retains a sparse phosphate-sugar--base scaffold and encodes nucleotide identity and local conformation in residue-wise latents. A shared flow network generates both jointly, and an RNA-specific decoder then reconstructs all heavy atoms. To expand supervision, we construct a quality-controlled corpus of 168,561 RNA structures, integrating experimental data with predictions from three folding models, including 10,631 MSA-supported structures generated in this work. La-Ribo improves designability and codesignability over the evaluated baselines across sampling budgets and two refolding models, and the same prior supports scaffold-conditioned inverse folding without additional training.

Protein family design emerges as a promising alternative by combining the advantages of de novo protein design and mutation-based directed evolution.In this paper, we propose ProfileBFN, the Profile Bayesian Flow Networks, for specifically generative modeling of protein families. ProfileBFN extends the discrete Bayesian Flow Network from an MSA profile perspective, which can be trained on single protein sequences by regarding it as a degenerate profile, thereby achieving efficient protein family design by avoiding large-scale MSA data construction and training. Empirical results show that ProfileBFN has a profound understanding of proteins. When generating diverse and novel family proteins, it can accurately capture the structural characteristics of the family. The enzyme produced by this method is more likely than the previous approach to have the corresponding function, offering better odds of generating diverse proteins with the desired functionality.

When interacting with highly dynamic environments, scene flow allows autonomous systems to reason about the non-rigid motion of multiple independent objects. This is of particular interest in the field of autonomous driving, in which many cars, people, bicycles, and other objects need to be accurately tracked. Current state-of-the-art methods require annotated scene flow data from autonomous driving scenes to train scene flow networks with supervised learning. As an alternative, we present a method of training scene flow that uses two self-supervised losses, based on nearest neighbors and cycle consistency. These self-supervised losses allow us to train our method on large unlabeled autonomous driving datasets; the resulting method matches current state-of-the-art supervised performance using no real world annotations and exceeds state-of-the-art performance when combining our self-supervised approach with supervised learning on a smaller labeled dataset.

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic processes to model approximate samples from these target densities. The main drawback of these approaches is that the training objective requires full trajectories to compute, resulting in sluggish credit assignment issues due to use of entire trajectories and a learning signal present only at the terminal time. In this work, we present Diffusion Generative Flow Samplers (DGFS), a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments, via parameterizing an additional "flow function". Our method takes inspiration from the theory developed for generative flow networks (GFlowNets), allowing us to make use of intermediate learning signals. Through various challenging experiments, we demonstrate that DGFS achieves more accurate estimates of the normalization constant than closely-related prior methods.

Generative modeling of crystal data distribution is an important yet challenging task due to the unique periodic physical symmetry of crystals. Diffusion-based methods have shown early promise in modeling crystal distribution. More recently, Bayesian Flow Networks were introduced to aggregate noisy latent variables, resulting in a variance-reduced parameter space that has been shown to be advantageous for modeling Euclidean data distributions with structural constraints (Song et al., 2023). Inspired by this, we seek to unlock its potential for modeling variables located in non-Euclidean manifolds e.g. those within crystal structures, by overcoming challenging theoretical issues. We introduce CrysBFN, a novel crystal generation method by proposing a periodic Bayesian flow, which essentially differs from the original Gaussian-based BFN by exhibiting non-monotonic entropy dynamics. To successfully realize the concept of periodic Bayesian flow, CrysBFN integrates a new entropy conditioning mechanism and empirically demonstrates its significance compared to time-conditioning. Extensive experiments over both crystal ab initio generation and crystal structure prediction tasks demonstrate the superiority of CrysBFN, which consistently achieves new state-of-the-art on all benchmarks. Surprisingly, we found that CrysBFN enjoys a significant improvement in sampling efficiency, e.g., ~100x speedup 10 v.s. 2000 steps network forwards) compared with previous diffusion-based methods on MP-20 dataset. Code is available at https://github.com/wu-han-lin/CrysBFN.

Unsupervised optical flow estimation is especially hard near occlusions and motion boundaries and in low-texture regions. We show that additional information such as semantics and domain knowledge can help better constrain this problem. We introduce SemARFlow, an unsupervised optical flow network designed for autonomous driving data that takes estimated semantic segmentation masks as additional inputs. This additional information is injected into the encoder and into a learned upsampler that refines the flow output. In addition, a simple yet effective semantic augmentation module provides self-supervision when learning flow and its boundaries for vehicles, poles, and sky. Together, these injections of semantic information improve the KITTI-2015 optical flow test error rate from 11.80% to 8.38%. We also show visible improvements around object boundaries as well as a greater ability to generalize across datasets. Code is available at https://github.com/duke-vision/semantic-unsup-flow-release.

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x.

Optical flow estimation is a classical yet challenging task in computer vision. One of the essential factors in accurately predicting optical flow is to alleviate occlusions between frames. However, it is still a thorny problem for current top-performing optical flow estimation methods due to insufficient local evidence to model occluded areas. In this paper, we propose the Super Kernel Flow Network (SKFlow), a CNN architecture to ameliorate the impacts of occlusions on optical flow estimation. SKFlow benefits from the super kernels which bring enlarged receptive fields to complement the absent matching information and recover the occluded motions. We present efficient super kernel designs by utilizing conical connections and hybrid depth-wise convolutions. Extensive experiments demonstrate the effectiveness of SKFlow on multiple benchmarks, especially in the occluded areas. Without pre-trained backbones on ImageNet and with a modest increase in computation, SKFlow achieves compelling performance and ranks 1st among currently published methods on the Sintel benchmark. On the challenging Sintel clean and final passes (test), SKFlow surpasses the best-published result in the unmatched areas (7.96 and 12.50) by 9.09% and 7.92%. The code is available at https://github.com/littlespray/SKFlow{https://github.com/littlespray/SKFlow}.

Scene flow estimation predicts the 3D motion at each point in successive LiDAR scans. This detailed, point-level, information can help autonomous vehicles to accurately predict and understand dynamic changes in their surroundings. Current state-of-the-art methods require annotated data to train scene flow networks and the expense of labeling inherently limits their scalability. Self-supervised approaches can overcome the above limitations, yet face two principal challenges that hinder optimal performance: point distribution imbalance and disregard for object-level motion constraints. In this paper, we propose SeFlow, a self-supervised method that integrates efficient dynamic classification into a learning-based scene flow pipeline. We demonstrate that classifying static and dynamic points helps design targeted objective functions for different motion patterns. We also emphasize the importance of internal cluster consistency and correct object point association to refine the scene flow estimation, in particular on object details. Our real-time capable method achieves state-of-the-art performance on the self-supervised scene flow task on Argoverse 2 and Waymo datasets. The code is open-sourced at https://github.com/KTH-RPL/SeFlow along with trained model weights.

Generative flow networks (GFlowNets) are a family of algorithms for training a sequential sampler of discrete objects under an unnormalized target density and have been successfully used for various probabilistic modeling tasks. Existing training objectives for GFlowNets are either local to states or transitions, or propagate a reward signal over an entire sampling trajectory. We argue that these alternatives represent opposite ends of a gradient bias-variance tradeoff and propose a way to exploit this tradeoff to mitigate its harmful effects. Inspired by the TD(lambda) algorithm in reinforcement learning, we introduce subtrajectory balance or SubTB(lambda), a GFlowNet training objective that can learn from partial action subsequences of varying lengths. We show that SubTB(lambda) accelerates sampler convergence in previously studied and new environments and enables training GFlowNets in environments with longer action sequences and sparser reward landscapes than what was possible before. We also perform a comparative analysis of stochastic gradient dynamics, shedding light on the bias-variance tradeoff in GFlowNet training and the advantages of subtrajectory balance.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects x with non-negative reward R(x). Learning objectives guarantee the GFlowNet samples x from the target distribution p^*(x) propto R(x) when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching p^*(x) in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward x, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

Generative Flow Networks (GFlowNets) are amortized sampling methods that learn a distribution over discrete objects proportional to their rewards. GFlowNets exhibit a remarkable ability to generate diverse samples, yet occasionally struggle to consistently produce samples with high rewards due to over-exploration on wide sample space. This paper proposes to train GFlowNets with local search, which focuses on exploiting high-rewarded sample space to resolve this issue. Our main idea is to explore the local neighborhood via backtracking and reconstruction guided by backward and forward policies, respectively. This allows biasing the samples toward high-reward solutions, which is not possible for a typical GFlowNet solution generation scheme, which uses the forward policy to generate the solution from scratch. Extensive experiments demonstrate a remarkable performance improvement in several biochemical tasks. Source code is available: https://github.com/dbsxodud-11/ls_gfn.

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates with probabilities proportional to a given reward. However, GFlowNets can only be used with a predefined scalar reward, which can be either computationally expensive or not directly accessible, in the case of multi-objective optimization (MOO) tasks for example. Moreover, to prioritize identifying high-reward candidates, the conventional practice is to raise the reward to a higher exponent, the optimal choice of which may vary across different environments. To address these issues, we propose Order-Preserving GFlowNets (OP-GFNs), which sample with probabilities in proportion to a learned reward function that is consistent with a provided (partial) order on the candidates, thus eliminating the need for an explicit formulation of the reward function. We theoretically prove that the training process of OP-GFNs gradually sparsifies the learned reward landscape in single-objective maximization tasks. The sparsification concentrates on candidates of a higher hierarchy in the ordering, ensuring exploration at the beginning and exploitation towards the end of the training. We demonstrate OP-GFN's state-of-the-art performance in single-objective maximization (totally ordered) and multi-objective Pareto front approximation (partially ordered) tasks, including synthetic datasets, molecule generation, and neural architecture search.

Generative flow networks (GFlowNets) are a method for learning a stochastic policy for generating compositional objects, such as graphs or strings, from a given unnormalized density by sequences of actions, where many possible action sequences may lead to the same object. We find previously proposed learning objectives for GFlowNets, flow matching and detailed balance, which are analogous to temporal difference learning, to be prone to inefficient credit propagation across long action sequences. We thus propose a new learning objective for GFlowNets, trajectory balance, as a more efficient alternative to previously used objectives. We prove that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution. In experiments on four distinct domains, we empirically demonstrate the benefits of the trajectory balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.

Large Language Model (LLM) Red-Teaming, which proactively identifies vulnerabilities of LLMs, is an essential process for ensuring safety. Finding effective and diverse attacks in red-teaming is important, but achieving both is challenging. Generative Flow Networks (GFNs) that perform distribution matching are a promising methods, but they are notorious for training instability and mode collapse. In particular, unstable rewards in red-teaming accelerate mode collapse. We propose Stable-GFN (S-GFN), which eliminates partition function Z estimation in GFN and reduces training instability. S-GFN avoids Z-estimation through pairwise comparisons and employs a robust masking methodology against noisy rewards. Additionally, we propose a fluency stabilizer to prevent the model from getting stuck in local optima that produce gibberish. S-GFN provides more stable training while maintaining the optimal policy of GFN. We demonstrate the overwhelming attack performance and diversity of S-GFN across various settings.

Generative Flow Networks (GFlowNets) excel at sampling diverse, high-reward objects. In many practical applications where active reward queries are infeasible, these models must be trained using static offline datasets. Prevailing training methods typically rely on a proxy model to provide reward feedback for online sampled trajectories. However, constructing a reliable proxy is often challenging due to data scarcity or high evaluation costs. While existing proxy-free approaches attempt to address this, they often impose coarse constraints that limit the model's ability to explore effectively. To overcome these limitations, we propose Trajectory-Distilled GFlowNet (TD-GFN), a novel proxy-free training framework. TD-GFN utilizes inverse reinforcement learning (IRL) to extract dense, transition-level edge rewards from offline trajectories, providing rich structural guidance for efficient exploration. Crucially, to ensure robustness, these rewards guide the policy indirectly through DAG pruning and prioritized backward sampling. This design ensures that gradient updates rely exclusively on ground-truth terminal rewards from the dataset, thereby preventing error propagation. Empirical results demonstrate that TD-GFN significantly outperforms a broad range of existing baselines in both convergence speed and sample quality, establishing a more robust and efficient paradigm for offline GFlowNet training.

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.

Dense and versatile image representations underpin the success of virtually all computer vision applications. However, state-of-the-art networks, such as transformers, produce low-resolution feature grids, which are suboptimal for dense prediction tasks. To address this limitation, we present FlowFeat, a high-resolution and multi-task feature representation. The key ingredient behind FlowFeat is a novel distillation technique that embeds a distribution of plausible apparent motions, or motion profiles. By leveraging optical flow networks and diverse video data, we develop an effective self-supervised training framework that statistically approximates the apparent motion. With its remarkable level of spatial detail, FlowFeat encodes a compelling degree of geometric and semantic cues while exhibiting high temporal consistency. Empirically, FlowFeat significantly enhances the representational power of five state-of-the-art encoders and alternative upsampling strategies across three dense tasks: video object segmentation, monocular depth estimation and semantic segmentation. Training FlowFeat is computationally inexpensive and robust to inaccurate flow estimation, remaining highly effective even when using unsupervised flow networks. Our work takes a step forward towards reliable and versatile dense image representations.

The recent advances in diffusion models have set an impressive milestone in many generation tasks. Trending works such as DALL-E2, Imagen, and Stable Diffusion have attracted great interest in academia and industry. Despite the rapid landscape changes, recent new approaches focus on extensions and performance rather than capacity, thus requiring separate models for separate tasks. In this work, we expand the existing single-flow diffusion pipeline into a multi-flow network, dubbed Versatile Diffusion (VD), that handles text-to-image, image-to-text, image-variation, and text-variation in one unified model. Moreover, we generalize VD to a unified multi-flow multimodal diffusion framework with grouped layers, swappable streams, and other propositions that can process modalities beyond images and text. Through our experiments, we demonstrate that VD and its underlying framework have the following merits: a) VD handles all subtasks with competitive quality; b) VD initiates novel extensions and applications such as disentanglement of style and semantic, image-text dual-guided generation, etc.; c) Through these experiments and applications, VD provides more semantic insights of the generated outputs. Our code and models are open-sourced at https://github.com/SHI-Labs/Versatile-Diffusion.

Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling up to bigger models. Previous methods mainly utilize the similarity decomposition and the associativity of matrix multiplication to devise linear-time attention mechanisms. They avoid degeneration of attention to a trivial distribution by reintroducing inductive biases such as the locality, thereby at the expense of model generality and expressiveness. In this paper, we linearize Transformers free from specific inductive biases based on the flow network theory. We cast attention as the information flow aggregated from the sources (values) to the sinks (results) through the learned flow capacities (attentions). Within this framework, we apply the property of flow conservation into attention and propose the Flow-Attention mechanism of linear complexity. By respectively conserving the incoming flow of sinks for source competition and the outgoing flow of sources for sink allocation, Flow-Attention inherently generates informative attentions without using specific inductive biases. Empowered by the Flow-Attention, Flowformer yields strong performance in linear time for wide areas, including long sequence, time series, vision, natural language, and reinforcement learning. The code and settings are available at this repository: https://github.com/thuml/Flowformer.

The growing popularity of generative flow networks (GFlowNets or GFNs) from a range of researchers with diverse backgrounds and areas of expertise necessitates a library that facilitates the testing of new features (e.g., training losses and training policies) against standard benchmark implementations, or on a set of common environments. We present torchgfn, a PyTorch library that aims to address this need. Its core contribution is a modular and decoupled architecture which treats environments, neural network modules, and training objectives as interchangeable components. This provides users with a simple yet powerful API to facilitate rapid prototyping and novel research. Multiple examples are provided, replicating and unifying published results. The library is available on GitHub (https://github.com/GFNOrg/torchgfn) and on pypi (https://pypi.org/project/torchgfn/).

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the power of the interaction order. This bottleneck limits its use in large-scale or real-time applications, forcing traditional tools to rely on heuristics to reduce the number of path candidates at the cost of potentially reduced accuracy. To overcome this limitation, we propose a comprehensive machine-learning-assisted framework that replaces exhaustive path searching with intelligent sampling via Generative Flow Networks. Applying such generative models to this domain presents significant challenges, particularly sparse rewards due to the rarity of valid paths, which can lead to convergence failures and trivial solutions when evaluating high-order interactions in complex environments. To ensure robust learning and efficient exploration, our framework incorporates three key architectural components. First, we implement an experience replay buffer to capture and retain rare valid paths. Second, we adopt a uniform exploratory policy to improve generalization and prevent the model from overfitting to simple geometries. Third, we apply a physics-based action masking strategy that filters out physically impossible paths before the model even considers them. As demonstrated in our experimental validation, the proposed model achieves substantial speedups over exhaustive search -- up to 10times faster on GPU and 1000times faster on CPU -- while maintaining high coverage accuracy and successfully uncovering complex propagation paths. The complete source code, tests, and tutorial are available at https://github.com/jeertmans/sampling-paths.

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from 3times3 to 870times6. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.

Enhancing low-resolution, low-frame-rate videos to high-resolution, high-frame-rate quality is essential for a seamless user experience, motivating advancements in Continuous Spatial-Temporal Video Super Resolution (C-STVSR). While prior methods employ Implicit Neural Representation (INR) for continuous encoding, they often struggle to capture the complexity of video data, relying on simple coordinate concatenation and pre-trained optical flow network for motion representation. Interestingly, we find that adding position encoding, contrary to common observations, does not improve-and even degrade performance. This issue becomes particularly pronounced when combined with pre-trained optical flow networks, which can limit the model's flexibility. To address these issues, we propose BF-STVSR, a C-STVSR framework with two key modules tailored to better represent spatial and temporal characteristics of video: 1) B-spline Mapper for smooth temporal interpolation, and 2) Fourier Mapper for capturing dominant spatial frequencies. Our approach achieves state-of-the-art PSNR and SSIM performance, showing enhanced spatial details and natural temporal consistency.

We propose the use of fractals as a means of efficient data augmentation. Specifically, we employ plasma fractals for adapting global image augmentation transformations into continuous local transforms. We formulate the diamond square algorithm as a cascade of simple convolution operations allowing efficient computation of plasma fractals on the GPU. We present the TorMentor image augmentation framework that is totally modular and deterministic across images and point-clouds. All image augmentation operations can be combined through pipelining and random branching to form flow networks of arbitrary width and depth. We demonstrate the efficiency of the proposed approach with experiments on document image segmentation (binarization) with the DIBCO datasets. The proposed approach demonstrates superior performance to traditional image augmentation techniques. Finally, we use extended synthetic binary text images in a self-supervision regiment and outperform the same model when trained with limited data and simple extensions.

Designing antibody sequences to better resemble those observed in natural human repertoires is a key challenge in biologics development. We introduce IgCraft: a multi-purpose model for paired human antibody sequence generation, built on Bayesian Flow Networks. IgCraft presents one of the first unified generative modeling frameworks capable of addressing multiple antibody sequence design tasks with a single model, including unconditional sampling, sequence inpainting, inverse folding, and CDR motif scaffolding. Our approach achieves competitive results across the full spectrum of these tasks while constraining generation to the space of human antibody sequences, exhibiting particular strengths in CDR motif scaffolding (grafting) where we achieve state-of-the-art performance in terms of humanness and preservation of structural properties. By integrating previously separate tasks into a single scalable generative model, IgCraft provides a versatile platform for sampling human antibody sequences under a variety of contexts relevant to antibody discovery and engineering. Model code and weights are publicly available at github.com/mgreenig/IgCraft.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Achieving both accuracy and diverse reasoning remains challenging for Large Language Models (LLMs) in complex domains like mathematics. A key bottleneck is evaluating intermediate reasoning steps to guide generation without costly human annotations. To address this, we first introduce a novel Process Reward Model (PRM) trained automatically using Monte Carlo Tree Search coupled with a similarity-based data augmentation technique, effectively capturing step-level reasoning quality. Leveraging this PRM, we then adapt Generative Flow Networks (GFlowNets) to operate at the reasoning step level. Unlike traditional reinforcement learning focused on maximizing a single reward, GFlowNets naturally sample diverse, high-quality solutions proportional to their rewards, as measured by our PRM. Empirical evaluation shows strong improvements in both accuracy and solution diversity on challenging mathematical benchmarks (e.g., +2.59% absolute accuracy on MATH Level 5 for Llama3.2-3B), with effective generalization to unseen datasets (+9.4\% absolute on SAT MATH). Furthermore, we benchmark our PRM against existing open-source reward models, demonstrating superior alignment with reasoning quality and more consistent guidance for downstream generation. Our work demonstrates the potential of PRM-guided, step-level GFlowNets for developing more robust and versatile mathematical reasoning in LLMs.

The framework of dominant learned video compression methods is usually composed of motion prediction modules as well as motion vector and residual image compression modules, suffering from its complex structure and error propagation problem. Approaches have been proposed to reduce the complexity by replacing motion prediction modules with implicit flow networks. Error propagation aware training strategy is also proposed to alleviate incremental reconstruction errors from previously decoded frames. Although these methods have brought some improvement, little attention has been paid to the framework itself. Inspired by the success of learned image compression through simplifying the framework with a single deep neural network, it is natural to expect a better performance in video compression via a simple yet appropriate framework. Therefore, we propose a framework to directly compress raw-pixel frames (rather than residual images), where no extra motion prediction module is required. Instead, an entropy model is used to estimate the spatiotemporal redundancy in a latent space rather than pixel level, which significantly reduces the complexity of the framework. Specifically, the whole framework is a compression module, consisting of a unified auto-encoder which produces identically distributed latents for all frames, and a spatiotemporal entropy estimation model to minimize the entropy of these latents. Experiments showed that the proposed method outperforms state-of-the-art (SOTA) performance under the metric of multiscale structural similarity (MS-SSIM) and achieves competitive results under the metric of PSNR.

We introduce AMix-1, a powerful protein foundation model built on Bayesian Flow Networks and empowered by a systematic training methodology, encompassing pretraining scaling laws, emergent capability analysis, in-context learning mechanism, and test-time scaling algorithm. To guarantee robust scalability, we establish a predictive scaling law and reveal the progressive emergence of structural understanding via loss perspective, culminating in a strong 1.7-billion model. Building on this foundation, we devise a multiple sequence alignment (MSA)-based in-context learning strategy to unify protein design into a general framework, where AMix-1 recognizes deep evolutionary signals among MSAs and consistently generates structurally and functionally coherent proteins. This framework enables the successful design of a dramatically improved AmeR variant with an up to 50times activity increase over its wild type. Pushing the boundaries of protein engineering, we further empower AMix-1 with an evolutionary test-time scaling algorithm for in silico directed evolution that delivers substantial, scalable performance gains as verification budgets are intensified, laying the groundwork for next-generation lab-in-the-loop protein design.

The emergence and popularity of facial deepfake methods spur the vigorous development of deepfake datasets and facial forgery detection, which to some extent alleviates the security concerns about facial-related artificial intelligence technologies. However, when it comes to human body forgery, there has been a persistent lack of datasets and detection methods, due to the later inception and complexity of human body generation methods. To mitigate this issue, we introduce TikTok-DeepFake (TT-DF), a novel large-scale diffusion-based dataset containing 6,120 forged videos with 1,378,857 synthetic frames, specifically tailored for body forgery detection. TT-DF offers a wide variety of forgery methods, involving multiple advanced human image animation models utilized for manipulation, two generative configurations based on the disentanglement of identity and pose information, as well as different compressed versions. The aim is to simulate any potential unseen forged data in the wild as comprehensively as possible, and we also furnish a benchmark on TT-DF. Additionally, we propose an adapted body forgery detection model, Temporal Optical Flow Network (TOF-Net), which exploits the spatiotemporal inconsistencies and optical flow distribution differences between natural data and forged data. Our experiments demonstrate that TOF-Net achieves favorable performance on TT-DF, outperforming current state-of-the-art extendable facial forgery detection models. For our TT-DF dataset, please refer to https://github.com/HashTAG00002/TT-DF.

We introduce RAFT-Stereo, a new deep architecture for rectified stereo based on the optical flow network RAFT. We introduce multi-level convolutional GRUs, which more efficiently propagate information across the image. A modified version of RAFT-Stereo can perform accurate real-time inference. RAFT-stereo ranks first on the Middlebury leaderboard, outperforming the next best method on 1px error by 29% and outperforms all published work on the ETH3D two-view stereo benchmark. Code is available at https://github.com/princeton-vl/RAFT-Stereo.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Diffusion models are capable of generating impressive images conditioned on text descriptions, and extensions of these models allow users to edit images at a relatively coarse scale. However, the ability to precisely edit the layout, position, pose, and shape of objects in images with diffusion models is still difficult. To this end, we propose motion guidance, a zero-shot technique that allows a user to specify dense, complex motion fields that indicate where each pixel in an image should move. Motion guidance works by steering the diffusion sampling process with the gradients through an off-the-shelf optical flow network. Specifically, we design a guidance loss that encourages the sample to have the desired motion, as estimated by a flow network, while also being visually similar to the source image. By simultaneously sampling from a diffusion model and guiding the sample to have low guidance loss, we can obtain a motion-edited image. We demonstrate that our technique works on complex motions and produces high quality edits of real and generated images.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Estimating camera motion and intrinsics from casual videos is a core challenge in computer vision. Traditional bundle-adjustment based methods, such as SfM and SLAM, struggle to perform reliably on arbitrary data. Although specialized SfM approaches have been developed for handling dynamic scenes, they either require intrinsics or computationally expensive test-time optimization and often fall short in performance. Recently, methods like Dust3r have reformulated the SfM problem in a more data-driven way. While such techniques show promising results, they are still 1) not robust towards dynamic objects and 2) require labeled data for supervised training. As an alternative, we propose AnyCam, a fast transformer model that directly estimates camera poses and intrinsics from a dynamic video sequence in feed-forward fashion. Our intuition is that such a network can learn strong priors over realistic camera poses. To scale up our training, we rely on an uncertainty-based loss formulation and pre-trained depth and flow networks instead of motion or trajectory supervision. This allows us to use diverse, unlabelled video datasets obtained mostly from YouTube. Additionally, we ensure that the predicted trajectory does not accumulate drift over time through a lightweight trajectory refinement step. We test AnyCam on established datasets, where it delivers accurate camera poses and intrinsics both qualitatively and quantitatively. Furthermore, even with trajectory refinement, AnyCam is significantly faster than existing works for SfM in dynamic settings. Finally, by combining camera information, uncertainty, and depth, our model can produce high-quality 4D pointclouds.

While the rapid adoption of multimodal generative models offers immense potential, it has also increased the risks of harmful content synthesis, deepfakes, and copyright infringements. To address these challenges, concept erasure has emerged as a prospective safeguard. However, as the field gradually transitions from U-Net-based diffusion models to Rectified Flow Transformers, erasure research has struggled to keep pace. In this work, we introduce GEM, a simple but highly effective erasure framework for Rectified Flow models. As part of our contribution, we establish a principled bridge between trajectory-based unlearning grounded in Generative Flow Networks and classic teacher-guided erasure: we translate trajectory-based signals into a teacher-guided flow-matching setup that unifies the strengths of both paradigms. Concretely, a teacher provides complementary attraction and repulsion signals that we combine into a single geometric guidance objective, yielding targeted suppression of unwanted concepts while preserving benign generation.

Recent advancements in large language models (LLMs) and their multimodal variants have led to remarkable progress across various domains, demonstrating impressive capabilities and unprecedented potential. In the era of ubiquitous connectivity, leveraging communication networks to distribute intelligence is a transformative concept, envisioning AI-powered services accessible at the network edge. However, pushing large models from the cloud to resource-constrained environments faces critical challenges. Model inference on low-end devices leads to excessive latency and performance bottlenecks, while raw data transmission over limited bandwidth networks causes high communication overhead. This article presents AI Flow, a framework that streamlines the inference process by jointly leveraging the heterogeneous resources available across devices, edge nodes, and cloud servers, making intelligence flow across networks. To facilitate cooperation among multiple computational nodes, the proposed framework explores a paradigm shift in the design of communication network systems from transmitting information flow to intelligence flow, where the goal of communications is task-oriented and folded into the inference process. Experimental results demonstrate the effectiveness of the proposed framework through an image captioning use case, showcasing the ability to reduce response latency while maintaining high-quality captions. This article serves as a position paper for identifying the motivation, challenges, and principles of AI Flow.

Free-flow road networks, such as suburban highways, are increasingly experiencing traffic congestion due to growing commuter inflow and limited infrastructure. Traditional control mechanisms, such as traffic signals or local heuristics, are ineffective or infeasible in these high-speed, signal-free environments. We introduce self-regulating cars, a reinforcement learning-based traffic control protocol that dynamically modulates vehicle speeds to optimize throughput and prevent congestion, without requiring new physical infrastructure. Our approach integrates classical traffic flow theory, gap acceptance models, and microscopic simulation into a physics-informed RL framework. By abstracting roads into super-segments, the agent captures emergent flow dynamics and learns robust speed modulation policies from instantaneous traffic observations. Evaluated in the high-fidelity PTV Vissim simulator on a real-world highway network, our method improves total throughput by 5%, reduces average delay by 13%, and decreases total stops by 3% compared to the no-control setting. It also achieves smoother, congestion-resistant flow while generalizing across varied traffic patterns, demonstrating its potential for scalable, ML-driven traffic management.

In this paper we propose WaveGlow: a flow-based network capable of generating high quality speech from mel-spectrograms. WaveGlow combines insights from Glow and WaveNet in order to provide fast, efficient and high-quality audio synthesis, without the need for auto-regression. WaveGlow is implemented using only a single network, trained using only a single cost function: maximizing the likelihood of the training data, which makes the training procedure simple and stable. Our PyTorch implementation produces audio samples at a rate of more than 500 kHz on an NVIDIA V100 GPU. Mean Opinion Scores show that it delivers audio quality as good as the best publicly available WaveNet implementation. All code will be made publicly available online.

Code clones are semantically similar code fragments pairs that are syntactically similar or different. Detection of code clones can help to reduce the cost of software maintenance and prevent bugs. Numerous approaches of detecting code clones have been proposed previously, but most of them focus on detecting syntactic clones and do not work well on semantic clones with different syntactic features. To detect semantic clones, researchers have tried to adopt deep learning for code clone detection to automatically learn latent semantic features from data. Especially, to leverage grammar information, several approaches used abstract syntax trees (AST) as input and achieved significant progress on code clone benchmarks in various programming languages. However, these AST-based approaches still can not fully leverage the structural information of code fragments, especially semantic information such as control flow and data flow. To leverage control and data flow information, in this paper, we build a graph representation of programs called flow-augmented abstract syntax tree (FA-AST). We construct FA-AST by augmenting original ASTs with explicit control and data flow edges. Then we apply two different types of graph neural networks (GNN) on FA-AST to measure the similarity of code pairs. As far as we have concerned, we are the first to apply graph neural networks on the domain of code clone detection. We apply our FA-AST and graph neural networks on two Java datasets: Google Code Jam and BigCloneBench. Our approach outperforms the state-of-the-art approaches on both Google Code Jam and BigCloneBench tasks.

Considering the complementarity of scene flow estimation in the spatial domain's focusing capability and 3D object tracking in the temporal domain's coherence, this study aims to address a comprehensive new task that can simultaneously capture fine-grained and long-term 3D motion in an online manner: long-term scene flow estimation (LSFE). We introduce SceneTracker, a novel learning-based LSFE network that adopts an iterative approach to approximate the optimal trajectory. Besides, it dynamically indexes and constructs appearance and depth correlation features simultaneously and employs the Transformer to explore and utilize long-range connections within and between trajectories. With detailed experiments, SceneTracker shows superior capabilities in handling 3D spatial occlusion and depth noise interference, highly tailored to the LSFE task's needs. Finally, we build the first real-world evaluation dataset, LSFDriving, further substantiating SceneTracker's commendable generalization capacity. The code and data for SceneTracker is available at https://github.com/wwsource/SceneTracker.

This paper presents the FlowTransformer framework, a novel approach for implementing transformer-based Network Intrusion Detection Systems (NIDSs). FlowTransformer leverages the strengths of transformer models in identifying the long-term behaviour and characteristics of networks, which are often overlooked by most existing NIDSs. By capturing these complex patterns in network traffic, FlowTransformer offers a flexible and efficient tool for researchers and practitioners in the cybersecurity community who are seeking to implement NIDSs using transformer-based models. FlowTransformer allows the direct substitution of various transformer components, including the input encoding, transformer, classification head, and the evaluation of these across any flow-based network dataset. To demonstrate the effectiveness and efficiency of the FlowTransformer framework, we utilise it to provide an extensive evaluation of various common transformer architectures, such as GPT 2.0 and BERT, on three commonly used public NIDS benchmark datasets. We provide results for accuracy, model size and speed. A key finding of our evaluation is that the choice of classification head has the most significant impact on the model performance. Surprisingly, Global Average Pooling, which is commonly used in text classification, performs very poorly in the context of NIDS. In addition, we show that model size can be reduced by over 50\%, and inference and training times improved, with no loss of accuracy, by making specific choices of input encoding and classification head instead of other commonly used alternatives.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

We propose a flow-guided transformer, which innovatively leverage the motion discrepancy exposed by optical flows to instruct the attention retrieval in transformer for high fidelity video inpainting. More specially, we design a novel flow completion network to complete the corrupted flows by exploiting the relevant flow features in a local temporal window. With the completed flows, we propagate the content across video frames, and adopt the flow-guided transformer to synthesize the rest corrupted regions. We decouple transformers along temporal and spatial dimension, so that we can easily integrate the locally relevant completed flows to instruct spatial attention only. Furthermore, we design a flow-reweight module to precisely control the impact of completed flows on each spatial transformer. For the sake of efficiency, we introduce window partition strategy to both spatial and temporal transformers. Especially in spatial transformer, we design a dual perspective spatial MHSA, which integrates the global tokens to the window-based attention. Extensive experiments demonstrate the effectiveness of the proposed method qualitatively and quantitatively. Codes are available at https://github.com/hitachinsk/FGT.

Video inpainting, which aims at filling in missing regions of a video, remains challenging due to the difficulty of preserving the precise spatial and temporal coherence of video contents. In this work we propose a novel flow-guided video inpainting approach. Rather than filling in the RGB pixels of each frame directly, we consider video inpainting as a pixel propagation problem. We first synthesize a spatially and temporally coherent optical flow field across video frames using a newly designed Deep Flow Completion network. Then the synthesized flow field is used to guide the propagation of pixels to fill up the missing regions in the video. Specifically, the Deep Flow Completion network follows a coarse-to-fine refinement to complete the flow fields, while their quality is further improved by hard flow example mining. Following the guide of the completed flow, the missing video regions can be filled up precisely. Our method is evaluated on DAVIS and YouTube-VOS datasets qualitatively and quantitatively, achieving the state-of-the-art performance in terms of inpainting quality and speed.

The increasing number of different, incompatible congestion control algorithms has led to an increased deployment of fair queuing. Fair queuing isolates each network flow and can thus guarantee fairness for each flow even if the flows' congestion controls are not inherently fair. So far, each queue in the fair queuing system either has a fixed, static maximum size or is managed by an Active Queue Management (AQM) algorithm like CoDel. In this paper we design an AQM mechanism (Learning Fair Qdisc (LFQ)) that dynamically learns the optimal buffer size for each flow according to a specified reward function online. We show that our Deep Learning based algorithm can dynamically assign the optimal queue size to each flow depending on its congestion control, delay and bandwidth. Comparing to competing fair AQM schedulers, it provides significantly smaller queues while achieving the same or higher throughput.

Machine comprehension (MC), answering a query about a given context paragraph, requires modeling complex interactions between the context and the query. Recently, attention mechanisms have been successfully extended to MC. Typically these methods use attention to focus on a small portion of the context and summarize it with a fixed-size vector, couple attentions temporally, and/or often form a uni-directional attention. In this paper we introduce the Bi-Directional Attention Flow (BIDAF) network, a multi-stage hierarchical process that represents the context at different levels of granularity and uses bi-directional attention flow mechanism to obtain a query-aware context representation without early summarization. Our experimental evaluations show that our model achieves the state-of-the-art results in Stanford Question Answering Dataset (SQuAD) and CNN/DailyMail cloze test.

A central task in virtual cell modeling is predicting single-cell transcriptional responses to unseen genetic perturbations and drug combinations, and biological networks provide valuable priors on gene relationships. Existing graph-based models commonly use the same network to structure gene representations and mediate intergene interactions, thereby implicitly treating stable associations as perturbation-response pathways. Gene Ontology and control-derived coexpression networks encode relatively stable relationships rather than intervention-specific response directions or magnitudes. We therefore propose GeneGeoFlow, which conditions a control-anchored residual flow on gene-wise geometry derived from biological networks to learn intervention-specific transcriptional responses. GeneGeoFlow derives multi-scale spectral coordinates from Gene Ontology and control-derived coexpression networks. A perturbation-conditioned, gene-wise gating module selects relevant structural scales and network sources, yielding intervention-specific gene geometry. The resulting geometry conditions a control-anchored residual flow without explicitly propagating target-derived signals along the graph. Condition-wise optimal transport couples unpaired control and perturbed populations for training, while a Delta-correlation objective aligns the predicted and observed condition-level expression-shift directions. GeneGeoFlow achieves Pearson Delta scores of 0.8979 on the Norman additive benchmark and 0.9088 on five held-out drug combinations in the fixed ComboSciPlex test split. These results support perturbation-conditioned gene geometry as an effective structural prior for intervention-specific response prediction, without conflating stable gene relationships with response propagation.

In this paper, we present a new inpainting framework for recovering missing regions of video frames. Compared with image inpainting, performing this task on video presents new challenges such as how to preserving temporal consistency and spatial details, as well as how to handle arbitrary input video size and length fast and efficiently. Towards this end, we propose a novel deep learning architecture which incorporates ConvLSTM and optical flow for modeling the spatial-temporal consistency in videos. It also saves much computational resource such that our method can handle videos with larger frame size and arbitrary length streamingly in real-time. Furthermore, to generate an accurate optical flow from corrupted frames, we propose a robust flow generation module, where two sources of flows are fed and a flow blending network is trained to fuse them. We conduct extensive experiments to evaluate our method in various scenarios and different datasets, both qualitatively and quantitatively. The experimental results demonstrate the superior of our method compared with the state-of-the-art inpainting approaches.

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models unfeasibly expensive in terms of parameters. We present an alternative parameterization scheme called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the concept of flow indication embedding, which are key missing components that enable density estimation from a single neural network. Experiments performed on audio and image models confirm that our method provides a new parameter-efficient solution for scalable NFs with significant sublinear parameter complexity.

We present AnaMoDiff, a novel diffusion-based method for 2D motion analogies that is applied to raw, unannotated videos of articulated characters. Our goal is to accurately transfer motions from a 2D driving video onto a source character, with its identity, in terms of appearance and natural movement, well preserved, even when there may be significant discrepancies between the source and driving characters in their part proportions and movement speed and styles. Our diffusion model transfers the input motion via a latent optical flow (LOF) network operating in a noised latent space, which is spatially aware, efficient to process compared to the original RGB videos, and artifact-resistant through the diffusion denoising process even amid dense movements. To accomplish both motion analogy and identity preservation, we train our denoising model in a feature-disentangled manner, operating at two noise levels. While identity-revealing features of the source are learned via conventional noise injection, motion features are learned from LOF-warped videos by only injecting noise with large values, with the stipulation that motion properties involving pose and limbs are encoded by higher-level features. Experiments demonstrate that our method achieves the best trade-off between motion analogy and identity preservation.

The continual growth of high speed networks is a challenge for real-time network analysis systems. The real time traffic classification is an issue for corporations and ISPs (Internet Service Providers). This work presents the design and implementation of a real time flow-based network traffic classification system. The classifier monitor acts as a pipeline consisting of three modules: packet capture and pre-processing, flow reassembly, and classification with Machine Learning (ML). The modules are built as concurrent processes with well defined data interfaces between them so that any module can be improved and updated independently. In this pipeline, the flow reassembly function becomes the bottleneck of the performance. In this implementation, was used a efficient method of reassembly which results in a average delivery delay of 0.49 seconds, approximately. For the classification module, the performances of the K-Nearest Neighbor (KNN), C4.5 Decision Tree, Naive Bayes (NB), Flexible Naive Bayes (FNB) and AdaBoost Ensemble Learning Algorithm are compared in order to validate our approach.

Video outpainting aims to expand the visible content of a video beyond the original frame boundaries while preserving spatial fidelity and temporal coherence across frames. Existing methods primarily rely on large-scale generative models, such as diffusion models. However, generationbased approaches suffer from implicit temporal modeling and limited spatial context. These limitations lead to intraframe and inter-frame inconsistencies, which become particularly pronounced in dynamic scenes and large outpainting scenarios. To overcome these challenges, we propose Seen-to-Scene, a novel framework that unifies propagationbased and generation-based paradigms for video outpainting. Specifically, Seen-to-Scene leverages flow-based propagation with a flow completion network pre-trained for video inpainting, which is fine-tuned in an end-to-end manner to bridge the domain gap and reconstruct coherent motion fields. To further improve the efficiency and reliability of propagation, we introduce a reference-guided latent propagation that effectively propagates source content across frames. Extensive experiments demonstrate that our method achieves superior temporal coherence and visual realism with efficient inference, surpassing even prior state-of-the-art methods that require input-specific adaptation.

Molecular glue degraders have emerged as a promising strategy for targeted protein degradation by inducing ternary complex formation between an E3 ubiquitin ligase and a target protein. Despite their therapeutic potential, computational design of molecular glues remains largely unexplored. Unlike conventional structure-based drug design, molecular glue design is governed by the unknown protein-protein interface and requires the simultaneous modeling of ligand generation, protein-protein docking, and ternary complex assembly. In this work, we formulate molecular glue design as a ternary complex generation problem and propose a biology-inspired generative framework, TriGlue. Motivated by the mechanism of molecular glue action, we decompose ternary complex generation into two coupled stages: interface estimation and interface-conditioned complex generation. First, we develop an SE(3)-equivariant interface estimation module that predicts a geometrically constrained protein-protein interface from unbound monomer structures. Second, we introduce an interface-conditioned ternary flow matching network that jointly generates the molecular glue and predicts the rigid-body transformation required to assemble the ternary complex. Extensive experiments demonstrate that TriGlue generates chemically valid molecules and produces plausible ternary complexes, which highlight the potential of biology-inspired generative modeling for accelerating molecular glue discovery. Our code is available at https://github.com/yuliangyan0807/molecular-glue-design.

Morphing techniques generate artificial biometric samples that combine features from multiple individuals, allowing each contributor to be verified against a single enrolled template. While extensively studied in face recognition, this vulnerability remains largely unexplored in voice biometrics. Prior work on voice morphing is computationally expensive, non-scalable, and limited to acoustically similar identity pairs, constraining practical deployment. Moreover, existing sound-morphing methods target audio textures, music, or environmental sounds and are not transferable to voice identity manipulation. We propose VoxMorph, a zero-shot framework that produces high-fidelity voice morphs from as little as five seconds of audio per subject without model retraining. Our method disentangles vocal traits into prosody and timbre embeddings, enabling fine-grained interpolation of speaking style and identity. These embeddings are fused via Spherical Linear Interpolation (Slerp) and synthesized using an autoregressive language model coupled with a Conditional Flow Matching network. VoxMorph achieves state-of-the-art performance, delivering a 2.6x gain in audio quality, a 73% reduction in intelligibility errors, and a 67.8% morphing attack success rate on automated speaker verification systems under strict security thresholds. This work establishes a practical and scalable paradigm for voice morphing with significant implications for biometric security. The code and dataset are available on our project page: https://vcbsl.github.io/VoxMorph/

Reliable traffic data are essential for understanding urban mobility and developing effective traffic management strategies. This study introduces the DRone-derived Intelligence For Traffic analysis (DRIFT) dataset, a large-scale urban traffic dataset collected systematically from synchronized drone videos at approximately 250 meters altitude, covering nine interconnected intersections in Daejeon, South Korea. DRIFT provides high-resolution vehicle trajectories that include directional information, processed through video synchronization and orthomap alignment, resulting in a comprehensive dataset of 81,699 vehicle trajectories. Through our DRIFT dataset, researchers can simultaneously analyze traffic at multiple scales - from individual vehicle maneuvers like lane-changes and safety metrics such as time-to-collision to aggregate network flow dynamics across interconnected urban intersections. The DRIFT dataset is structured to enable immediate use without additional preprocessing, complemented by open-source models for object detection and trajectory extraction, as well as associated analytical tools. DRIFT is expected to significantly contribute to academic research and practical applications, such as traffic flow analysis and simulation studies. The dataset and related resources are publicly accessible at https://github.com/AIxMobility/The-DRIFT.

Pan-sharpening aims to generate a high-resolution multispectral (HRMS) image by integrating the spectral information of a low-resolution multispectral (LRMS) image with the texture details of a high-resolution panchromatic (PAN) image. It essentially inherits the ill-posed nature of the super-resolution (SR) task that diverse HRMS images can degrade into an LRMS image. However, existing deep learning-based methods recover only one HRMS image from the LRMS image and PAN image using a deterministic mapping, thus ignoring the diversity of the HRMS image. In this paper, to alleviate this ill-posed issue, we propose a flow-based pan-sharpening network (PanFlowNet) to directly learn the conditional distribution of HRMS image given LRMS image and PAN image instead of learning a deterministic mapping. Specifically, we first transform this unknown conditional distribution into a given Gaussian distribution by an invertible network, and the conditional distribution can thus be explicitly defined. Then, we design an invertible Conditional Affine Coupling Block (CACB) and further build the architecture of PanFlowNet by stacking a series of CACBs. Finally, the PanFlowNet is trained by maximizing the log-likelihood of the conditional distribution given a training set and can then be used to predict diverse HRMS images. The experimental results verify that the proposed PanFlowNet can generate various HRMS images given an LRMS image and a PAN image. Additionally, the experimental results on different kinds of satellite datasets also demonstrate the superiority of our PanFlowNet compared with other state-of-the-art methods both visually and quantitatively.

In this paper we propose Flowtron: an autoregressive flow-based generative network for text-to-speech synthesis with control over speech variation and style transfer. Flowtron borrows insights from IAF and revamps Tacotron in order to provide high-quality and expressive mel-spectrogram synthesis. Flowtron is optimized by maximizing the likelihood of the training data, which makes training simple and stable. Flowtron learns an invertible mapping of data to a latent space that can be manipulated to control many aspects of speech synthesis (pitch, tone, speech rate, cadence, accent). Our mean opinion scores (MOS) show that Flowtron matches state-of-the-art TTS models in terms of speech quality. In addition, we provide results on control of speech variation, interpolation between samples and style transfer between speakers seen and unseen during training. Code and pre-trained models will be made publicly available at https://github.com/NVIDIA/flowtron

Camera traps, unmanned observation devices, and deep learning-based image recognition systems have greatly reduced human effort in collecting and analyzing wildlife images. However, data collected via above apparatus exhibits 1) long-tailed and 2) open-ended distribution problems. To tackle the open-set long-tailed recognition problem, we propose the Temporal Flow Mask Attention Network that comprises three key building blocks: 1) an optical flow module, 2) an attention residual module, and 3) a meta-embedding classifier. We extract temporal features of sequential frames using the optical flow module and learn informative representation using attention residual blocks. Moreover, we show that applying the meta-embedding technique boosts the performance of the method in open-set long-tailed recognition. We apply this method on a Korean Demilitarized Zone (DMZ) dataset. We conduct extensive experiments, and quantitative and qualitative analyses to prove that our method effectively tackles the open-set long-tailed recognition problem while being robust to unknown classes.

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.

Learning to solve complex tasks with signal temporal logic (STL) specifications is crucial to many real-world applications. However, most previous works only consider fixed or parametrized STL specifications due to the lack of a diverse STL dataset and encoders to effectively extract temporal logic information for downstream tasks. In this paper, we propose TeLoGraF, Temporal Logic Graph-encoded Flow, which utilizes Graph Neural Networks (GNN) encoder and flow-matching to learn solutions for general STL specifications. We identify four commonly used STL templates and collect a total of 200K specifications with paired demonstrations. We conduct extensive experiments in five simulation environments ranging from simple dynamical models in the 2D space to high-dimensional 7DoF Franka Panda robot arm and Ant quadruped navigation. Results show that our method outperforms other baselines in the STL satisfaction rate. Compared to classical STL planning algorithms, our approach is 10-100X faster in inference and can work on any system dynamics. Besides, we show our graph-encoding method's capability to solve complex STLs and robustness to out-distribution STL specifications. Code is available at https://github.com/mengyuest/TeLoGraF

Training large and highly accurate deep learning (DL) models is computationally costly. This cost is in great part due to the excessive number of trained parameters, which are well-known to be redundant and compressible for the execution phase. This paper proposes a novel transformation which changes the topology of the DL architecture such that it reaches an optimal cross-layer connectivity. This transformation leverages our important observation that for a set level of accuracy, convergence is fastest when network topology reaches the boundary of a Small-World Network. Small-world graphs are known to possess a specific connectivity structure that enables enhanced signal propagation among nodes. Our small-world models, called SWNets, provide several intriguing benefits: they facilitate data (gradient) flow within the network, enable feature-map reuse by adding long-range connections and accommodate various network architectures/datasets. Compared to densely connected networks (e.g., DenseNets), SWNets require a substantially fewer number of training parameters while maintaining a similar level of classification accuracy. We evaluate our networks on various DL model architectures and image classification datasets, namely, CIFAR10, CIFAR100, and ILSVRC (ImageNet). Our experiments demonstrate an average of ~2.1x improvement in convergence speed to the desired accuracy

Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully connected layers, it is often less effective for convolutional layers. This lack of success of dropout for convolutional layers is perhaps due to the fact that activation units in convolutional layers are spatially correlated so information can still flow through convolutional networks despite dropout. Thus a structured form of dropout is needed to regularize convolutional networks. In this paper, we introduce DropBlock, a form of structured dropout, where units in a contiguous region of a feature map are dropped together. We found that applying DropbBlock in skip connections in addition to the convolution layers increases the accuracy. Also, gradually increasing number of dropped units during training leads to better accuracy and more robust to hyperparameter choices. Extensive experiments show that DropBlock works better than dropout in regularizing convolutional networks. On ImageNet classification, ResNet-50 architecture with DropBlock achieves 78.13% accuracy, which is more than 1.6% improvement on the baseline. On COCO detection, DropBlock improves Average Precision of RetinaNet from 36.8% to 38.4%.

Detector simulation and event reconstruction will be computationally expensive for future e^+e^- collider programs and are currently critical bottlenecks for accurate feasibility studies. To address this challenge, we build a Parnassus model for the CLD detector concept. Parnassus is a framework for automatically tuning a surrogate model, in our case, a conditional flow matching neural network, to emulate a full detector simulation and reconstruction. We train on e^+e^-to Zto qbar q events at s=91.2 GeV processed through a Geant4 simulation of the CLD detector concept and the Pandora particle-flow reconstruction and reproduce single-particle kinematics, particle-IDs, and impact-parameter distributions. We also examine jet- and event-level features, inclusively and split by flavor, and find excellent fidelity, significantly better than the parameterized program Delphes. Furthermore, we train a transformer-based flavor tagger on the reconstructed particle-flow constituents and show that the surrogate preserves the b/c/s/q discrimination of the full CLD reconstruction. The Parnassus CLD model achieves a generation cost of about 1.2 ms (40 ms) per event on a single GPU (CPU), over three (two) orders of magnitude faster than full simulation and reconstruction. Our model is publicly available for feasibility and design studies.

Pruning generates sparse networks by setting parameters to zero. In this work we improve one-shot pruning methods, applied before training, without adding any additional storage costs while preserving the sparse gradient computations. The main difference to pruning is that we do not sparsify the network's weights but learn just a few key parameters and keep the other ones fixed at their random initialized value. This mechanism is called freezing the parameters. Those frozen weights can be stored efficiently with a single 32bit random seed number. The parameters to be frozen are determined one-shot by a single for- and backward pass applied before training starts. We call the introduced method FreezeNet. In our experiments we show that FreezeNets achieve good results, especially for extreme freezing rates. Freezing weights preserves the gradient flow throughout the network and consequently, FreezeNets train better and have an increased capacity compared to their pruned counterparts. On the classification tasks MNIST and CIFAR-10/100 we outperform SNIP, in this setting the best reported one-shot pruning method, applied before training. On MNIST, FreezeNet achieves 99.2% performance of the baseline LeNet-5-Caffe architecture, while compressing the number of trained and stored parameters by a factor of x 157.

Flow matching has emerged as a scalable paradigm for training high-quality generative models, but sampling from the learned probability flow requires many network evaluations. Distillation can reduce this cost to one or a few evaluations; however, one-step generation often sacrifices quality, making few-step generation the practical operating regime. Existing few-step methods perform their iterative computation along the probability flow and therefore require a fixed, manually chosen timestep discretization. This discretization is often chosen heuristically and is expensive to tune; it may also be restrictive when refinement difficulty differs across samples or spatial locations. We introduce data-space iteration, a few-step generation framework that removes flow discretization altogether. Starting from noise, a shared generator directly refines its prediction in data space, with every iteration trained to produce the best sample permitted by its capacity. Our formulation integrates with distribution matching distillation (DMD) with minimal changes, enabling a controlled comparison between iteration methods under matched training settings. On class-conditional ImageNet 256x256, data-space iteration outperforms standard discretization baselines and matches or improves upon variants selected through schedule search, without requiring schedule-specific training. These results show that data-space iteration provides a simple and effective alternative to discretized flow-space iteration for fast generation.

Given a piece of text, a video clip, and a reference audio, the movie dubbing task aims to generate speech that aligns with the video while cloning the desired voice. The existing methods have two primary deficiencies: (1) They struggle to simultaneously hold audio-visual sync and achieve clear pronunciation; (2) They lack the capacity to express user-defined emotions. To address these problems, we propose EmoDubber, an emotion-controllable dubbing architecture that allows users to specify emotion type and emotional intensity while satisfying high-quality lip sync and pronunciation. Specifically, we first design Lip-related Prosody Aligning (LPA), which focuses on learning the inherent consistency between lip motion and prosody variation by duration level contrastive learning to incorporate reasonable alignment. Then, we design Pronunciation Enhancing (PE) strategy to fuse the video-level phoneme sequences by efficient conformer to improve speech intelligibility. Next, the speaker identity adapting module aims to decode acoustics prior and inject the speaker style embedding. After that, the proposed Flow-based User Emotion Controlling (FUEC) is used to synthesize waveform by flow matching prediction network conditioned on acoustics prior. In this process, the FUEC determines the gradient direction and guidance scale based on the user's emotion instructions by the positive and negative guidance mechanism, which focuses on amplifying the desired emotion while suppressing others. Extensive experimental results on three benchmark datasets demonstrate favorable performance compared to several state-of-the-art methods.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are considered: 1. interpretability of machine-learned results, 2. bulking out of training data, and 3. generalizability of neural networks. For the interpretability, we first demonstrate two methods to observe the internal procedure of neural networks, i.e., visualization of hidden layers and application of gradient-weighted class activation mapping (Grad-CAM), applied to canonical fluid flow estimation problems -- (1) drag coefficient estimation of a cylinder wake and (2) velocity estimation from particle images. It is exemplified that both approaches can successfully tell us evidences of the great capability of machine learning-based estimations. We then utilize some techniques to bulk out training data for super-resolution analysis and temporal prediction for cylinder wake and NOAA sea surface temperature data to demonstrate that sufficient training of neural networks with limited amount of training data can be achieved for fluid flow problems. The generalizability of machine learning model is also discussed by accounting for the perspectives of inter/extrapolation of training data, considering super-resolution of wakes behind two parallel cylinders. We find that various flow patterns generated by complex interaction between two cylinders can be reconstructed well, even for the test configurations regarding the distance factor. The present paper can be a significant step toward practical uses of neural networks for both laminar and turbulent flow problems.

A network-based approach is presented to investigate the cerebrovascular flow patterns during atrial fibrillation (AF) with respect to normal sinus rhythm (NSR). AF, the most common cardiac arrhythmia with faster and irregular beating, has been recently and independently associated with the increased risk of dementia. However, the underlying hemodynamic mechanisms relating the two pathologies remain mainly undetermined so far; thus the contribution of modeling and refined statistical tools is valuable. Pressure and flow rate temporal series in NSR and AF are here evaluated along representative cerebral sites (from carotid arteries to capillary brain circulation), exploiting reliable artificially built signals recently obtained from an in silico approach. The complex network analysis evidences, in a synthetic and original way, a dramatic signal variation towards the distal/capillary cerebral regions during AF, which has no counterpart in NSR conditions. At the large artery level, networks obtained from both AF and NSR hemodynamic signals exhibit elongated and chained features, which are typical of pseudo-periodic series. These aspects are almost completely lost towards the microcirculation during AF, where the networks are topologically more circular and present random-like characteristics. As a consequence, all the physiological phenomena at microcerebral level ruled by periodicity - such as regular perfusion, mean pressure per beat, and average nutrient supply at cellular level - can be strongly compromised, since the AF hemodynamic signals assume irregular behaviour and random-like features. Through a powerful approach which is complementary to the classical statistical tools, the present findings further strengthen the potential link between AF hemodynamic and cognitive decline.

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present DeepWeightFlow, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by DeepWeightFlow do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

Traditional neural network approaches for traffic flow forecasting are usually single task learning (STL) models, which do not take advantage of the information provided by related tasks. In contrast to STL, multitask learning (MTL) has the potential to improve generalization by transferring information in training signals of extra tasks. In this paper, MTL based neural networks are used for traffic flow forecasting. For neural network MTL, a backpropagation (BP) network is constructed by incorporating traffic flows at several contiguous time instants into an output layer. Nodes in the output layer can be seen as outputs of different but closely related STL tasks. Comprehensive experiments on urban vehicular traffic flow data and comparisons with STL show that MTL in BP neural networks is a promising and effective approach for traffic flow forecasting.

Institutional investors have been increasing the allocation of the illiquid alternative assets such as private equity funds in their portfolios, yet there exists a very limited literature on cash flow forecasting of illiquid alternative assets. The net cash flow of private equity funds typically follow a J-curve pattern, however the timing and the size of the contributions and distributions depend on the investment opportunities. In this paper, we develop a benchmark model and present two novel approaches (direct vs. indirect) to predict the cash flows of private equity funds. We introduce a sliding window approach to apply on our cash flow data because different vintage year funds contain different lengths of cash flow information. We then pass the data to an LSTM/ GRU model to predict the future cash flows either directly or indirectly (based on the benchmark model). We further integrate macroeconomic indicators into our data, which allows us to consider the impact of market environment on cash flows and to apply stress testing. Our results indicate that the direct model is easier to implement compared to the benchmark model and the indirect model, but still the predicted cash flows align better with the actual cash flows. We also show that macroeconomic variables improve the performance of the direct model whereas the impact is not obvious on the indirect model.

Understanding the motion states of the surrounding environment is critical for safe autonomous driving. These motion states can be accurately derived from scene flow, which captures the three-dimensional motion field of points. Existing LiDAR scene flow methods extract spatial features from each point cloud and then fuse them channel-wise, resulting in the implicit extraction of spatio-temporal features. Furthermore, they utilize 2D Bird's Eye View and process only two frames, missing crucial spatial information along the Z-axis and the broader temporal context, leading to suboptimal performance. To address these limitations, we propose Flow4D, which temporally fuses multiple point clouds after the 3D intra-voxel feature encoder, enabling more explicit extraction of spatio-temporal features through a 4D voxel network. However, while using 4D convolution improves performance, it significantly increases the computational load. For further efficiency, we introduce the Spatio-Temporal Decomposition Block (STDB), which combines 3D and 1D convolutions instead of using heavy 4D convolution. In addition, Flow4D further improves performance by using five frames to take advantage of richer temporal information. As a result, the proposed method achieves a 45.9% higher performance compared to the state-of-the-art while running in real-time, and won 1st place in the 2024 Argoverse 2 Scene Flow Challenge. The code is available at https://github.com/dgist-cvlab/Flow4D.

Predicting the motion of multiple traffic participants has always been one of the most challenging tasks in autonomous driving. The recently proposed occupancy flow field prediction method has shown to be a more effective and scalable representation compared to general trajectory prediction methods. However, in complex multi-agent traffic scenarios, it remains difficult to model the interactions among various factors and the dependencies among prediction outputs at different time steps. In view of this, we propose a transformer-based hierarchical feature guided network (HGNET), which can efficiently extract features of agents and map information from visual and vectorized inputs, modeling multimodal interaction relationships. Second, we design the Feature-Guided Attention (FGAT) module to leverage the potential guiding effects between different prediction targets, thereby improving prediction accuracy. Additionally, to enhance the temporal consistency and causal relationships of the predictions, we propose a Time Series Memory framework to learn the conditional distribution models of the prediction outputs at future time steps from multivariate time series. The results demonstrate that our model exhibits competitive performance, which ranks 3rd in the 2024 Waymo Occupancy and Flow Prediction Challenge.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.

Numerical simulations in industrial applications often require performing numerous high-precision computations parameterized by specific experimental conditions. For instance, in vehicle body design, aerodynamic simulations are essential for evaluating the aerodynamic characteristics of various proposed body geometries. However, computational resource constraints often become a bottleneck. Therefore, achieving the desired accuracy while minimizing computational cost is crucial. To address this challenge, model reduction methods have been developed to decrease the degrees of freedom by constraining the possible states of a physical system to a lower-dimensional subspace. In particular, reduction techniques that project the system onto a nonlinear subspace using neural networks have been actively studied. Our previous research developed a reduced-order model that integrates neural-network-based model reduction with a time-evolution method, implemented as a distributed parallel training framework to process high-resolution flow field data efficiently. In this study, we extend this reduction approach by incorporating a variational autoencoder to assess its robustness in high-Reynolds-number flows around multiple vehicle bodies with varying geometries. Specifically, we evaluate the reconstruction accuracy of vortex generation across different spatial and temporal scales using a compact latent representation, with a particular focus on the flow behavior near the rear end of the vehicle body.

Recent work has shown that optical flow estimation can be formulated as a supervised learning task and can be successfully solved with convolutional networks. Training of the so-called FlowNet was enabled by a large synthetically generated dataset. The present paper extends the concept of optical flow estimation via convolutional networks to disparity and scene flow estimation. To this end, we propose three synthetic stereo video datasets with sufficient realism, variation, and size to successfully train large networks. Our datasets are the first large-scale datasets to enable training and evaluating scene flow methods. Besides the datasets, we present a convolutional network for real-time disparity estimation that provides state-of-the-art results. By combining a flow and disparity estimation network and training it jointly, we demonstrate the first scene flow estimation with a convolutional network.

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, truncated domains, which introduce non-negligible errors and limit applicability in real-world scenarios. In this study, we propose a novel framework utilizing Physics-Informed Neural Networks (PINNs) to solve the full nonlinear compressible potential equation in an unbounded (infinite) domain. We address the unbounded-domain and convergence challenges inherent in standard PINNs by incorporating a coordinate transformation and embedding physical asymptotic constraints directly into the network architecture. Furthermore, we employ a Multi-Stage PINN (MS-PINN) approach to iteratively minimize residuals, achieving solution accuracy approaching machine precision. We validate this framework by simulating flow over circular and elliptical geometries, comparing our results against traditional finite-domain and linearized solutions. Our findings quantify the noticeable discrepancies introduced by domain truncation and linearization, particularly at higher Mach numbers, and demonstrate that this new framework is a robust, high-fidelity tool for computational fluid dynamics.

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and curvature of feature flow along the neural network, which implicitly increases the sparsity of the parameters. The principle behind FFR is that coherent and smooth evolution of features will lead to an efficient network that avoids redundant parameters. The high structured sparsity obtained from FFR enables us to prune filters effectively. Experiments with VGGNets, ResNets on CIFAR-10/100, and Tiny ImageNet datasets demonstrate that FFR can significantly improve both unstructured and structured sparsity. Our pruning results in terms of reduction of parameters and FLOPs are comparable to or even better than those of state-of-the-art pruning methods.

Traffic forecasting has emerged as a core component of intelligent transportation systems. However, timely accurate traffic forecasting, especially long-term forecasting, still remains an open challenge due to the highly nonlinear and dynamic spatial-temporal dependencies of traffic flows. In this paper, we propose a novel paradigm of Spatial-Temporal Transformer Networks (STTNs) that leverages dynamical directed spatial dependencies and long-range temporal dependencies to improve the accuracy of long-term traffic forecasting. Specifically, we present a new variant of graph neural networks, named spatial transformer, by dynamically modeling directed spatial dependencies with self-attention mechanism to capture realtime traffic conditions as well as the directionality of traffic flows. Furthermore, different spatial dependency patterns can be jointly modeled with multi-heads attention mechanism to consider diverse relationships related to different factors (e.g. similarity, connectivity and covariance). On the other hand, the temporal transformer is utilized to model long-range bidirectional temporal dependencies across multiple time steps. Finally, they are composed as a block to jointly model the spatial-temporal dependencies for accurate traffic prediction. Compared to existing works, the proposed model enables fast and scalable training over a long range spatial-temporal dependencies. Experiment results demonstrate that the proposed model achieves competitive results compared with the state-of-the-arts, especially forecasting long-term traffic flows on real-world PeMS-Bay and PeMSD7(M) datasets.

We propose a novel scene flow estimation approach to capture and infer 3D motions from point clouds. Estimating 3D motions for point clouds is challenging, since a point cloud is unordered and its density is significantly non-uniform. Such unstructured data poses difficulties in matching corresponding points between point clouds, leading to inaccurate flow estimation. We propose a novel architecture named Sparse Convolution-Transformer Network (SCTN) that equips the sparse convolution with the transformer. Specifically, by leveraging the sparse convolution, SCTN transfers irregular point cloud into locally consistent flow features for estimating continuous and consistent motions within an object/local object part. We further propose to explicitly learn point relations using a point transformer module, different from exiting methods. We show that the learned relation-based contextual information is rich and helpful for matching corresponding points, benefiting scene flow estimation. In addition, a novel loss function is proposed to adaptively encourage flow consistency according to feature similarity. Extensive experiments demonstrate that our proposed approach achieves a new state of the art in scene flow estimation. Our approach achieves an error of 0.038 and 0.037 (EPE3D) on FlyingThings3D and KITTI Scene Flow respectively, which significantly outperforms previous methods by large margins.

Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and memory demand required by CFD codes may become very high for flows of practical interest, such as in aerodynamic shape optimization. This expense is associated with the complexity of the fluid flow governing equations, which include non-linear partial derivative terms that are of difficult solution, leading to long computational times and limiting the number of hypotheses that can be tested during the process of iterative design. Therefore, we propose DeepCFD: a convolutional neural network (CNN) based model that efficiently approximates solutions for the problem of non-uniform steady laminar flows. The proposed model is able to learn complete solutions of the Navier-Stokes equations, for both velocity and pressure fields, directly from ground-truth data generated using a state-of-the-art CFD code. Using DeepCFD, we found a speedup of up to 3 orders of magnitude compared to the standard CFD approach at a cost of low error rates.

As camera-based documents are increasingly used, the rectification of distorted document images becomes a need to improve the recognition performance. In this paper, we propose a novel framework for both rectifying distorted document image and removing background finely, by estimating pixel-wise displacements using a fully convolutional network (FCN). The document image is rectified by transformation according to the displacements of pixels. The FCN is trained by regressing displacements of synthesized distorted documents, and to control the smoothness of displacements, we propose a Local Smooth Constraint (LSC) in regularization. Our approach is easy to implement and consumes moderate computing resource. Experiments proved that our approach can dewarp document images effectively under various geometric distortions, and has achieved the state-of-the-art performance in terms of local details and overall effect.

As the Internet rapidly expands, the increasing complexity and diversity of network activities pose significant challenges to effective network governance and security regulation. Network traffic, which serves as a crucial data carrier of network activities, has become indispensable in this process. Network traffic detection aims to monitor, analyze, and evaluate the data flows transmitted across the network to ensure network security and optimize performance. However, existing network traffic detection methods generally suffer from several limitations: 1) a narrow focus on characterizing traffic features from a single perspective; 2) insufficient exploration of discriminative features for different traffic; 3) poor generalization to different traffic scenarios. To address these issues, we propose a multi-view correlation-aware framework named FlowID for network traffic detection. FlowID captures multi-view traffic features via temporal and interaction awareness, while a hypergraph encoder further explores higher-order relationships between flows. To overcome the challenges of data imbalance and label scarcity, we design a dual-contrastive proxy task, enhancing the framework's ability to differentiate between various traffic flows through traffic-to-traffic and group-to-group contrast. Extensive experiments on five real-world datasets demonstrate that FlowID significantly outperforms existing methods in accuracy, robustness, and generalization across diverse network scenarios, particularly in detecting malicious traffic.

Prior works on event-based optical flow estimation have investigated several gradient-based learning methods to train neural networks for predicting optical flow. However, they do not utilize the fast data rate of event data streams and rely on a spatio-temporal representation constructed from a collection of events over a fixed period of time (often between two grayscale frames). As a result, optical flow is only evaluated at a frequency much lower than the rate data is produced by an event-based camera, leading to a temporally sparse optical flow estimation. To predict temporally dense optical flow, we cast the problem as a sequential learning task and propose a training methodology to train sequential networks for continuous prediction on an event stream. We propose two types of networks: one focused on performance and another focused on compute efficiency. We first train long-short term memory networks (LSTMs) on the DSEC dataset and demonstrated 10x temporally dense optical flow estimation over existing flow estimation approaches. The additional benefit of having a memory to draw long temporal correlations back in time results in a 19.7% improvement in flow prediction accuracy of LSTMs over similar networks with no memory elements. We subsequently show that the inherent recurrence of spiking neural networks (SNNs) enables them to learn and estimate temporally dense optical flow with 31.8% lesser parameters than LSTM, but with a slightly increased error. This demonstrates potential for energy-efficient implementation of fast optical flow prediction using SNNs.

The FlowNet demonstrated that optical flow estimation can be cast as a learning problem. However, the state of the art with regard to the quality of the flow has still been defined by traditional methods. Particularly on small displacements and real-world data, FlowNet cannot compete with variational methods. In this paper, we advance the concept of end-to-end learning of optical flow and make it work really well. The large improvements in quality and speed are caused by three major contributions: first, we focus on the training data and show that the schedule of presenting data during training is very important. Second, we develop a stacked architecture that includes warping of the second image with intermediate optical flow. Third, we elaborate on small displacements by introducing a sub-network specializing on small motions. FlowNet 2.0 is only marginally slower than the original FlowNet but decreases the estimation error by more than 50%. It performs on par with state-of-the-art methods, while running at interactive frame rates. Moreover, we present faster variants that allow optical flow computation at up to 140fps with accuracy matching the original FlowNet.

Video-to-audio (V2A) generation aims to synthesize content-matching audio from silent video, and it remains challenging to build V2A models with high generation quality, efficiency, and visual-audio temporal synchrony. We propose Frieren, a V2A model based on rectified flow matching. Frieren regresses the conditional transport vector field from noise to spectrogram latent with straight paths and conducts sampling by solving ODE, outperforming autoregressive and score-based models in terms of audio quality. By employing a non-autoregressive vector field estimator based on a feed-forward transformer and channel-level cross-modal feature fusion with strong temporal alignment, our model generates audio that is highly synchronized with the input video. Furthermore, through reflow and one-step distillation with guided vector field, our model can generate decent audio in a few, or even only one sampling step. Experiments indicate that Frieren achieves state-of-the-art performance in both generation quality and temporal alignment on VGGSound, with alignment accuracy reaching 97.22%, and 6.2% improvement in inception score over the strong diffusion-based baseline. Audio samples are available at http://frieren-v2a.github.io.

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

This paper proposes a novel framework to predict traffic flows' bandwidth ahead of time. Modern network management systems share a common issue: the network situation evolves between the moment the decision is made and the moment when actions (countermeasures) are applied. This framework converts packets from real-life traffic into flows containing relevant features. Machine learning models, including Decision Tree, Random Forest, XGBoost, and Deep Neural Network, are trained on these data to predict the bandwidth at the next time instance for every flow. Predictions can be fed to the management system instead of current flows bandwidth in order to take decisions on a more accurate network state. Experiments were performed on 981,774 flows and 15 different time windows (from 0.03s to 4s). They show that the Random Forest is the best performing and most reliable model, with a predictive performance consistently better than relying on the current bandwidth (+19.73% in mean absolute error and +18.00% in root mean square error). Experimental results indicate that this framework can help network management systems to take more informed decisions using a predicted network state.