Generative Modeling with Flux Matching

2026-05-08

AI Summary

Traditional score-based generative models are constrained by the requirement to learn a conservative vector field—namely, the data score—which limits the flexibility of dynamical design. This work proposes Flux Matching, a novel paradigm that redefines the generative vector field as a designable variable rather than a fixed target, enabling the use of arbitrary non-conservative vector fields that admit the desired stationary distribution. This formulation facilitates the incorporation of inductive biases, structural priors, and directional dependencies, thereby allowing more flexible modeling of ODE/SDE dynamics. Empirical results demonstrate that the proposed framework not only accelerates sampling in high-dimensional image generation but also explicitly encodes causal relationships among variables, enhancing model interpretability.

Abstract

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.

Problem

• generative modeling
• score-based models
• vector fields
• stationary distribution
• inductive biases

Innovation

• Flux Matching
• generative modeling
• non-conservative vector fields
• score-based models
• stationary distribution