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Training deep neural networks remains computationally intensive due to the itera2 tive nature of gradient-based optimization. We propose Gradient Flow Matching (GFM), a continuous-time modeling framework that treats neural network training…

Machine Learning · Computer Science 2025-05-27 Xiao Shou , Yanna Ding , Jianxi Gao

Diffusion models have recently shown promise in offline RL. However, these methods often suffer from high training costs and slow convergence, particularly when using transformer-based denoising backbones. While several optimization…

Machine Learning · Computer Science 2025-06-23 Zhiying Qiu , Tao Lin

Reinforcement Learning (RL) algorithms aim to learn an optimal policy by iteratively sampling actions to learn how to maximize the total expected return, $R(x)$. GFlowNets are a special class of algorithms designed to generate diverse…

Machine Learning · Computer Science 2023-07-19 Nikhil Vemgal , Elaine Lau , Doina Precup

Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…

Disordered Systems and Neural Networks · Physics 2024-03-04 Artan Sheshmani , Yi-Zhuang You , Baturalp Buyukates , Amir Ziashahabi , Salman Avestimehr

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…

Machine Learning · Computer Science 2025-12-02 Mudit Gaur , Prashant Trivedi , Shuchin Aeron , Amrit Singh Bedi , George K. Atia , Vaneet Aggarwal

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

Machine Learning · Computer Science 2021-11-10 Kaifeng Lyu , Zhiyuan Li , Runzhe Wang , Sanjeev Arora

We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…

Machine Learning · Computer Science 2021-09-13 Chulhee Yun , Shankar Krishnan , Hossein Mobahi

This paper investigates the accuracy of generative models and the impact of knowledge transfer on their generation precision. Specifically, we examine a generative model for a target task, fine-tuned using a pre-trained model from a source…

Machine Learning · Statistics 2025-06-03 Xinyu Tian , Xiaotong Shen

An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed. We first utilize the Cram\'er-Rao bound to identify the Gaussian setting as a fundamental…

Information Theory · Computer Science 2026-02-10 Qiang Sun , H. Vincent Poor , Wenyi Zhang

Taming diffusion models for generative segmentation has attracted increasing attention. While existing approaches primarily focus on architectural tweaks or training heuristics, there remains a limited understanding of the intrinsic…

Computer Vision and Pattern Recognition · Computer Science 2026-03-20 Chaoyang Wang , Yaobo Liang , Boci Peng , Fan Duan , Jingdong Wang , Yunhai Tong

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based…

Machine Learning · Statistics 2025-06-30 Xiuyuan Cheng , Jianfeng Lu , Yixin Tan , Yao Xie

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

Machine Learning · Computer Science 2024-04-25 Felix Draxler , Peter Sorrenson , Lea Zimmermann , Armand Rousselot , Ullrich Köthe

Stochastic gradient descent (SGD), one of the most fundamental optimization algorithms in machine learning (ML), can be recast through a continuous-time approximation as a Fokker-Planck equation for Langevin dynamics, a viewpoint that has…

Machine Learning · Statistics 2025-08-19 Hiroshi Horii , Sothea Has

Generative Flow Networks (GFlowNets) enable structured generation with inherent diversity, but existing sampling strategies often rely on weak guided exploration, slowing early discovery of high-reward candidates. In tasks such as molecular…

Machine Learning · Computer Science 2026-02-03 Rui Zhu , Yudong Zhang , Xuan Yu , Chen Zhang , Xu Wang , Yang Wang

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…

Machine Learning · Computer Science 2024-03-12 Dinghuai Zhang , Ricky T. Q. Chen , Cheng-Hao Liu , Aaron Courville , Yoshua Bengio

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…

Computer Vision and Pattern Recognition · Computer Science 2016-12-07 Eddy Ilg , Nikolaus Mayer , Tonmoy Saikia , Margret Keuper , Alexey Dosovitskiy , Thomas Brox

Flow-based models learn a target distribution by modeling a marginal velocity field, defined as the average of sample-wise velocities connecting each sample from a simple prior to the target data. When sample-wise velocities conflict at the…

Computer Vision and Pattern Recognition · Computer Science 2026-04-07 Yeonwoo Cha , Jaehoon Yoo , Semin Kim , Yunseo Park , Jinhyeon Kwon , Seunghoon Hong

Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…

Computer Vision and Pattern Recognition · Computer Science 2019-08-20 Hao Li , Hong Zhang , Xiaojuan Qi , Ruigang Yang , Gao Huang

Implicit generative modeling (IGM) aims to produce samples of synthetic data matching the characteristics of a target data distribution. Recent work (e.g. score-matching networks, diffusion models) has approached the IGM problem from the…

Machine Learning · Computer Science 2026-05-21 Romann M. Weber

Discriminator Guidance has become a popular method for efficiently refining pre-trained Score-Matching Diffusion models. However, in this paper, we demonstrate that the standard implementation of this technique does not necessarily lead to…

Machine Learning · Computer Science 2025-06-12 Alexandre Verine , Ahmed Mehdi Inane , Florian Le Bronnec , Benjamin Negrevergne , Yann Chevaleyre