Papers › How to build a consistency model: Learning flow maps via self-distillation

How to build a consistency model: Learning flow maps via self-distillation

24 May 2025arXiv:2505.18825archive 2025-07-28

Nicholas M. Boffi, Michael S. Albergo, Eric Vanden-Eijnden

Building on the framework proposed in Boffi et al. (2024), we present a systematic approach for learning flow maps associated with flow and diffusion models. Flow map-based models, commonly known as consistency models, encompass recent efforts to improve the efficiency of generative models based on solutions to differential equations. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert existing distillation schemes into direct training algorithms via self-distillation, eliminating the need for pre-trained models. We empirically evaluate several instantiations of our framework, finding that high-dimensional tasks like image synthesis benefit from objective functions that avoid temporal and spatial derivatives of the flow map, while lower-dimensional tasks can benefit from objectives incorporating higher-order derivatives to capture sharp features.

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