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This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…

Machine Learning · Computer Science 2024-07-23 Heli Ben-Hamu , Omri Puny , Itai Gat , Brian Karrer , Uriel Singer , Yaron Lipman

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the…

Computer Vision and Pattern Recognition · Computer Science 2025-10-09 Anirban Samaddar , Yixuan Sun , Viktor Nilsson , Sandeep Madireddy

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…

Computer Vision and Pattern Recognition · Computer Science 2020-11-17 Hyeongju Kim , Hyeonseung Lee , Woo Hyun Kang , Joun Yeop Lee , Nam Soo Kim

We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…

Statistics Theory · Mathematics 2021-10-22 Xingyu Zhou , Yuling Jiao , Jin Liu , Jian Huang

Generative models have gained more and more attention in recent years for their remarkable success in tasks that required estimating and sampling data distribution to generate high-fidelity synthetic data. In speech, text-to-speech…

Audio and Speech Processing · Electrical Eng. & Systems 2024-03-27 Alexander H. Liu , Matt Le , Apoorv Vyas , Bowen Shi , Andros Tjandra , Wei-Ning Hsu

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

Computer Vision and Pattern Recognition · Computer Science 2026-03-10 Yucheng Xing , Xiaodong Liu , Xin Wang

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Machine Learning · Statistics 2026-03-11 Shinto Eguchi

We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a…

Machine Learning · Computer Science 2019-04-23 Micha Livne , David Fleet

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods…

Computer Vision and Pattern Recognition · Computer Science 2023-07-18 Quan Dao , Hao Phung , Binh Nguyen , Anh Tran

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been…

Machine Learning · Computer Science 2023-12-11 Qinqing Zheng , Matt Le , Neta Shaul , Yaron Lipman , Aditya Grover , Ricky T. Q. Chen

Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…

Computer Vision and Pattern Recognition · Computer Science 2022-12-15 Kangfu Mei , Nithin Gopalakrishnan Nair , Vishal M. Patel

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…

Computer Vision and Pattern Recognition · Computer Science 2023-09-06 Mohsen Zand , Ali Etemad , Michael Greenspan

Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is…

Machine Learning · Computer Science 2025-06-16 Kevin Rojas , Yuchen Zhu , Sichen Zhu , Felix X. -F. Ye , Molei Tao

We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned…

Machine Learning · Computer Science 2026-04-14 Shanchuan Lin , Ceyuan Yang , Zhijie Lin , Hao Chen , Haoqi Fan

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…

Machine Learning · Computer Science 2026-03-19 Peter Holderrieth , Ezra Erives

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…

Computer Vision and Pattern Recognition · Computer Science 2025-12-23 Junho Lee , Kwanseok Kim , Joonseok Lee

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

Machine Learning · Computer Science 2026-05-06 Aaron Havens , Brian Karrer , Neta Shaul

In this work, we propose FlowTime, a generative model for probabilistic forecasting of multivariate timeseries data. Given historical measurements and optional future covariates, we formulate forecasting as sampling from a learned…

Machine Learning · Computer Science 2026-02-10 Ahmed ElGazzar , Marcel van Gerven