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The vision community is undergoing the unprecedented progress with the emergence of Vision-Language Pretraining Models (VLMs). Prompt learning plays as the holy grail of accessing VLMs since it enables their fast adaptation to downstream…

Computer Vision and Pattern Recognition · Computer Science 2025-11-04 Ziliang Chen , Xin Huang , Quanlong Guan , Liang Lin , Weiqi Luo

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be…

Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…

Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…

Machine Learning · Statistics 2022-03-17 Gianluigi Silvestri , Emily Fertig , Dave Moore , Luca Ambrogioni

We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…

Machine Learning · Computer Science 2025-09-29 Maojiang Su , Mingcheng Lu , Jerry Yao-Chieh Hu , Shang Wu , Zhao Song , Alex Reneau , Han Liu

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Machine Learning · Computer Science 2026-02-03 Yuhao Huang , Taos Transue , Shih-Hsin Wang , William Feldman , Hong Zhang , Bao Wang

Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…

Machine Learning · Statistics 2024-06-07 Andrew Campbell , Jason Yim , Regina Barzilay , Tom Rainforth , Tommi Jaakkola

With the advent of score-matching techniques for model training and Langevin dynamics for sample generation, energy-based models (EBMs) have gained renewed interest as generative models. Recent EBMs usually use neural networks to define…

Machine Learning · Computer Science 2025-05-05 Yukun Li , Li-Ping Liu

This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the…

Machine Learning · Statistics 2020-04-02 Ruiqi Gao , Erik Nijkamp , Diederik P. Kingma , Zhen Xu , Andrew M. Dai , Ying Nian Wu

Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows, making them less…

Machine Learning · Statistics 2020-07-23 Jianfei Chen , Cheng Lu , Biqi Chenli , Jun Zhu , Tian Tian

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Machine Learning · Computer Science 2023-12-07 Gavin Kerrigan , Giosue Migliorini , Padhraic Smyth

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have…

Computation and Language · Computer Science 2025-03-10 Minkai Xu , Tomas Geffner , Karsten Kreis , Weili Nie , Yilun Xu , Jure Leskovec , Stefano Ermon , Arash Vahdat

Controllable generation is one of the key requirements for successful adoption of deep generative models in real-world applications, but it still remains as a great challenge. In particular, the compositional ability to generate novel…

Computer Vision and Pattern Recognition · Computer Science 2021-12-07 Weili Nie , Arash Vahdat , Anima Anandkumar

Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…

Machine Learning · Computer Science 2026-02-05 Arip Asadulaev , Semyon Semenov , Abduragim Shtanchaev , Eric Moulines , Fakhri Karray , Martin Takac

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data…

Computer Vision and Pattern Recognition · Computer Science 2023-10-13 Jiali Cui , Ying Nian Wu , Tian Han

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the…

Machine Learning · Computer Science 2022-02-25 Léo Gagnon , Guillaume Lajoie

Conditional Flow Matching (CFM) models can generate high-quality samples from a non-informative prior, but they can be slow, often needing hundreds of network evaluations (NFE). To address this, we propose Implicit Dynamical Flow Fusion…

Machine Learning · Computer Science 2025-05-28 Mohammad R. Rezaei , Milos R. Popovic , Milad Lankarany , Rahul G. Krishnan

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as…

Machine Learning · Computer Science 2025-11-27 Utkarsh Utkarsh , Pengfei Cai , Alan Edelman , Rafael Gomez-Bombarelli , Christopher Vincent Rackauckas

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

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the…

Machine Learning · Statistics 2019-11-27 Erik Nijkamp , Mitch Hill , Song-Chun Zhu , Ying Nian Wu