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Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. A key development is the reformulation of the reverse sampling process as a deterministic probability flow…

Machine Learning · Computer Science 2025-08-15 Daniel Zhengyu Huang , Jiaoyang Huang , Zhengjiang Lin

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Machine Learning · Computer Science 2023-02-09 Yaron Lipman , Ricky T. Q. Chen , Heli Ben-Hamu , Maximilian Nickel , Matt Le

Diffusion models, which have been advancing rapidly in recent years, may generate samples that closely resemble the training data. This phenomenon, known as memorization, may lead to copyright issues. In this study, we propose a method to…

Machine Learning · Computer Science 2025-03-26 Masaya Hasegawa , Koji Yasuda

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can…

Machine Learning · Computer Science 2024-11-01 Shahar Yadin , Noam Elata , Tomer Michaeli

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…

Machine Learning · Computer Science 2025-02-07 Youssef Marzouk , Zhi Ren , Jakob Zech

Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…

Machine Learning · Statistics 2026-05-08 Meira Iske , Carola-Bibiane Schönlieb

Identifying Out-of-distribution (OOD) data is becoming increasingly critical as the real-world applications of deep learning methods expand. Post-hoc methods modify softmax scores fine-tuned on outlier data or leverage intermediate feature…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Saandeep Aathreya , Shaun Canavan

Denoising diffusion probabilistic models (DDPMs) are a class of powerful generative models. The past few years have witnessed the great success of DDPMs in generating high-fidelity samples. A significant limitation of the DDPMs is the slow…

Computer Vision and Pattern Recognition · Computer Science 2023-04-25 Yansong Gao , Zhihong Pan , Xin Zhou , Le Kang , Pratik Chaudhari

The diffusion model has demonstrated promising results in image generation, recently becoming mainstream and representing a notable advancement for many generative modeling tasks. Prior applications of the diffusion model for both fast…

Instrumentation and Detectors · Physics 2025-06-18 Cheng Jiang , Sitian Qian , Huilin Qu

We compare the discretize-optimize (Disc-Opt) and optimize-discretize (Opt-Disc) approaches for time-series regression and continuous normalizing flows (CNFs) using neural ODEs. Neural ODEs are ordinary differential equations (ODEs) with…

Machine Learning · Computer Science 2020-08-03 Derek Onken , Lars Ruthotto

Continuous normalizing flows (CNFs) can model data distributions with expressive infinite-length architectures. But this modeling involves computationally expensive process of solving an ordinary differential equation (ODE) during maximum…

Machine Learning · Computer Science 2024-10-15 Denis Gudovskiy , Tomoyuki Okuno , Yohei Nakata

Foundation models enable prompt-based classifiers for zero-shot and few-shot learning. Nonetheless, the conventional method of employing fixed prompts suffers from distributional shifts that negatively impact generalizability to unseen…

Machine Learning · Computer Science 2024-10-29 Yingjun Du , Gaowen Liu , Yuzhang Shang , Yuguang Yao , Ramana Kompella , Cees G. M. Snoek

Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…

Methodology · Statistics 2021-07-12 Alex Akira Okuno , Felipe Maia Polo

Normalizing flows are prominent deep generative models that provide tractable probability distributions and efficient density estimation. However, they are well known to fail while detecting Out-of-Distribution (OOD) inputs as they directly…

Machine Learning · Computer Science 2021-11-17 Nishant Kumar , Pia Hanfeld , Michael Hecht , Michael Bussmann , Stefan Gumhold , Nico Hoffmann

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Computer Vision and Pattern Recognition · Computer Science 2024-08-26 Defang Chen , Zhenyu Zhou , Jian-Ping Mei , Chunhua Shen , Chun Chen , Can Wang

Normalization is an important and vastly investigated technique in deep learning. However, its role for Ordinary Differential Equation based networks (neural ODEs) is still poorly understood. This paper investigates how different…

Machine Learning · Computer Science 2020-04-29 Julia Gusak , Larisa Markeeva , Talgat Daulbaev , Alexandr Katrutsa , Andrzej Cichocki , Ivan Oseledets

Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model…

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we…

Machine Learning · Computer Science 2025-11-04 François Rozet , Gérôme Andry , François Lanusse , Gilles Louppe

Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these…

Machine Learning · Statistics 2022-07-13 Florentin Coeurdoux , Nicolas Dobigeon , Pierre Chainais

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…

Machine Learning · Computer Science 2025-02-20 Zijing Ou , Mingtian Zhang , Andi Zhang , Tim Z. Xiao , Yingzhen Li , David Barber