Conservative Flows: A New Paradigm of Generative Models

2026-05-07

AI Summary

This work proposes a novel generative paradigm that circumvents the limitations of conventional models, which rely on mapping from a noise prior to data and often fail to preserve the intrinsic characteristics of the true data distribution. Instead, the approach leverages discrete stochastic dynamics that leave the data distribution invariant, initializing directly from the data support set. By integrating probability-conserving sampling with Metropolis-adjusted Langevin dynamics and predictor-corrector flows, the method operates directly on existing pretrained flow model checkpoints without requiring retraining, thereby enhancing sampling quality universally. Empirical evaluations on Swiss-roll, ImageNet-256, and Oxford Flowers-102 demonstrate consistent and significant improvements in generation fidelity over standard sampling techniques.

Abstract

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

Problem

• generative models
• conservative flows
• stochastic dynamics
• data distribution invariance
• noise prior

Innovation

• Conservative Flows
• invariant stochastic dynamics
• probability-preserving sampling
• Metropolis-adjusted Langevin
• predictor-corrector flow