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

• URL: http://arxiv.org/abs/2505.18825v1
• Date: Sat, 24 May 2025 18:50:50 GMT
• Title: How to build a consistency model: Learning flow maps via self-distillation
• Authors: Nicholas M. Boffi, Michael S. Albergo, Eric Vanden-Eijnden,
• Abstract summary: We present a systematic approach for learning flow maps associated with flow and diffusion models.<n>We exploit a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map.<n>We show how to convert existing distillation schemes into direct training algorithms via self-distillation.
• Score: 15.520853806024943
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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