Stabilizing Consistency Training: A Flow Map Analysis and Self-Distillation

TL;DR

This paper analyzes the stability issues of consistency models using flow map theory, and proposes a self-distillation approach to improve training stability and convergence across generative and policy learning tasks.

Contribution

It provides a theoretical flow map perspective on consistency models, and introduces a reformulated self-distillation method to enhance training stability and applicability.

Findings

Flow map analysis clarifies stability and convergence issues.

Self-distillation improves training stability and avoids degenerate solutions.

Method extends to diffusion-based policy learning without pretrained models.

Abstract

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.