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Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

Computer Vision and Pattern Recognition · Computer Science 2026-03-19 Liangyu Yuan , Ruoyu Wang , Tong Zhao , Dingwen Fu , Mingkun Lei , Beier Zhu , Chi Zhang

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Statistics Theory · Mathematics 2024-07-12 Xicheng Zhang

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…

Computer Vision and Pattern Recognition · Computer Science 2026-03-24 Yu Zhang , Xingzhuo Guo , Haoran Xu , Jialong Wu , Mingsheng Long

Aligning diffusion models with user preferences has been a key challenge. Existing methods for aligning diffusion models either require retraining or are limited to differentiable reward functions. To address these limitations, we propose a…

Computer Vision and Pattern Recognition · Computer Science 2025-02-28 Po-Hung Yeh , Kuang-Huei Lee , Jun-Cheng Chen

Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence. In particular, reward fine-tuning of diffusion and flow matching models and…

Machine Learning · Computer Science 2024-10-29 Carles Domingo-Enrich

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

Artificial Intelligence · Computer Science 2025-01-22 Masatoshi Uehara , Yulai Zhao , Chenyu Wang , Xiner Li , Aviv Regev , Sergey Levine , Tommaso Biancalani

This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. While diffusion models are widely known to provide excellent generative modeling capability, practical…

Machine Learning · Computer Science 2024-07-19 Masatoshi Uehara , Yulai Zhao , Tommaso Biancalani , Sergey Levine

Diffusion-based planning, learning, and control methods present a promising branch of powerful and expressive decision-making solutions. Given the growing interest, such methods have undergone numerous refinements over the past years.…

Machine Learning · Computer Science 2025-02-19 Dom Huh , Prasant Mohapatra

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true…

Machine Learning · Computer Science 2025-07-03 Thibaut Issenhuth , Sangchul Lee , Ludovic Dos Santos , Jean-Yves Franceschi , Chansoo Kim , Alain Rakotomamonjy

Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we…

Machine Learning · Computer Science 2026-02-05 Sedjro Salomon Hotegni , Sebastian Peitz

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow-…

Computer Vision and Pattern Recognition · Computer Science 2025-06-18 Amirmojtaba Sabour , Sanja Fidler , Karsten Kreis

Diffusion and flow-matching models scale because pretraining is supervised regression: a clean sample is noised analytically, and a model regresses against a closed-form target. RL post-training aligns the model with a reward. In image…

Machine Learning · Computer Science 2026-05-19 Andreas Bergmeister , Stefanie Jegelka , Nikolas Nüsken , Carles Domingo-Enrich , Jakiw Pidstrigach

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Machine Learning · Statistics 2024-03-08 Gen Li , Yuting Wei , Yuxin Chen , Yuejie Chi

Adapting large-scale foundation flow and diffusion generative models to optimize task-specific objectives while preserving prior information is crucial for real-world applications such as molecular design, protein docking, and creative…

Machine Learning · Computer Science 2025-12-01 Riccardo De Santi , Marin Vlastelica , Ya-Ping Hsieh , Zebang Shen , Niao He , Andreas Krause

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely…

Computer Vision and Pattern Recognition · Computer Science 2026-02-06 Junwan Kim , Jiho Park , Seonghu Jeon , Seungryong Kim

Aligning diffusion model outputs with downstream objectives is essential for improving task-specific performance. Broadly, inference-time training-free approaches for aligning diffusion models can be categorized into two main strategies:…

Computer Vision and Pattern Recognition · Computer Science 2025-12-16 Maurya Goyal , Anuj Singh , Hadi Jamali-Rad

There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC…

Optimization and Control · Mathematics 2026-03-24 Yuhang Mei , Amirhossein Taghvaei

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Machine Learning · Computer Science 2024-10-21 Runjia Li , Qiwei Di , Quanquan Gu

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Machine Learning · Computer Science 2024-08-06 Gen Li , Yuting Wei , Yuejie Chi , Yuxin Chen

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences --…

Computer Vision and Pattern Recognition · Computer Science 2025-03-13 Yihong Luo , Tianyang Hu , Yifan Song , Jiacheng Sun , Zhenguo Li , Jing Tang