How to build a consistency model: Learning flow maps via self-distillation
Nicholas Boffi, Michael Albergo, Eric Vanden-Eijnden
We present a systematic approach for learning the flow map associated with a flow or diffusion model. The class of flow map-based models, commonly referred to as consistency models, encompasses a wide range of recent efforts to improve the efficiency of generative models based on the solution of a differential equation. By exploiting a relation between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert a broad class of existing distillation schemes into single network direct training algorithms via the concept of self-distillation. We empirically study the performance of several instantiations of our framework, where we find that high-dimensional tasks such as image synthesis benefit from the design of objective functions that avoid temporal and spatial derivatives of the flow map, while for low-dimensional tasks requiring precision, objectives with higher-order derivatives can help capture sharp features.