Skip to content
#machine learning Preprint Open access

Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching

Denis Blessing Lorenz Richter Julius Berner Egor Malitskiy Gerhard Neumann
Oct 2026
Machine Learning

Abstract

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations, called Bridge Matching Sampler (BMS). Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse and further stabilize training. Empirically, we demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.

View source

Similar papers

#artificial intelligence Conference Open access Jun 2018

Gibson Env: Real-World Perception for Embodied Agents

This paper investigates developing real-world perception for active agents, proposes Gibson Environment for this purpose, and showcases a set of perceptual tasks learned therein.

F. Xia, Amir Zamir, Zhi-Yang He et al. · 1,069 citations · ⚡112
#machine learning Review Open access Oct 2014

Software development in startup companies: A systematic mapping study

The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.

Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al. · 394 citations · ⚡54

Diffusion models as plug-and-play priors

The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.

Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al. · 316 citations · ⚡15

Trajectory Balance: Improved Credit Assignment in GFlowNets

It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequenc...

Esmeralda S. Whitammer, Moksh Jain, Emmanuel Bengio et al. · 302 citations · ⚡60

KTO: Model Alignment as Prospect Theoretic Optimization

This work proposes a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, and suggests that the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.

Kawin Ethayarajh, Winnie Xu, Niklas Muennighoff et al. · 195 citations · ⚡28

Related blog posts

We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.