Joint Flow Matching for Generator-Consistent Classification

2026-07-26

AI Summary

Existing flow matching approaches struggle to jointly model forward generation and reverse classification of multivariate data, lacking consistency in conditional inference. This work proposes a Joint Flow Matching (JFM) framework that assigns symmetric roles to variables at temporal endpoints, thereby constructing a shared joint distribution such that forward and backward integrations naturally correspond to conditional forms of the same joint distribution. JFM is the first method to enable consistent bidirectional conditional inference within continuous normalizing flows, inherently supporting confidence calibration without post-processing and providing an interpretable foundation for discriminative–generative tasks. Experiments demonstrate that JFM achieves competitive classification accuracy on conditional datasets, generates samples highly consistent with the classifier, and yields natively calibrated confidence scores.

Abstract

We introduce Joint Flow Matching (JFM), a training framework for continuous normalising flows over multiple variables. Standard flow matching transports variables from noise to data simultaneously, offering no natural mechanism for forward and reverse conditional inference from a shared joint model. JFM resolves this by assigning opposite roles to each variable at the temporal endpoints. We prove that JFM produces a consistent joint distribution where that forward or reverse integration are conditionals of the same joint. We explore this consistency in the context of joint classification and generation as the basis for interpretability in discriminative-generative models. We validate JFM on conditional datasets producing competitive accuracy with inherently well-calibrated confidence scores without post-hoc calibration, and classifier-consistent image generation.

Problem

• flow matching
• conditional inference
• joint distribution
• generative modeling
• classifier-consistent generation

Innovation

• Joint Flow Matching
• continuous normalizing flows
• conditional inference
• generator-consistent classification
• well-calibrated confidence