Generative Modeling with Flux Matching

TL;DR

Flux Matching introduces a flexible generative modeling framework that generalizes score-based models by allowing non-conservative vector fields, enabling diverse applications like faster sampling and interpretable models.

Contribution

It proposes Flux Matching, a novel paradigm that relaxes score matching constraints, allowing direct design of vector fields for improved generative modeling.

Findings

Performs strongly on high-dimensional image datasets.

Enables faster sampling and interpretable models.

Supports dynamics with directed dependencies.

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.