The Discretization Complexity Analysis of Consistency Models under Variance Exploding Forward Process
Keywords: Discretization Complexity, Consistency Model
Abstract: Consistency models, a new class of one-step generative models, have shown state-of-the-art performance in one-step generation and achieve competitive performance compared to multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the diffusion process and trains a consistency function to map any point at any discretized timepoint of the diffusion process to the data distribution. Despite the empirical success, only a few works focus on the discretization complexity of consistency models. However, the setting of those works is far away from the empirical consistency models with good performance, suffers from large discretization complexity, and fails to explain the empirical success of consistency models. To bridge the gap between theory and application, we analyze consistency models with two key properties: (1) variance exploding forward process and (2) gradually decay discretization stepsize, which are both widely used in empirical consistency models. Under the above realistic setting, we make the first step to explain the empirical success of consistency models and achieve the state-of-the-art discretization complexity for consistency models, which is competitive with the results of diffusion models. After obtaining the results of the one-step sampling method of consistency models, we further analyze a multi-step consistency sampling algorithm proposed by \citet{song2023consistency} and show that this algorithm improves the discretization complexity compared with one-step generation, which matches the empirical observation.
Primary Area: generative models
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Submission Number: 3617
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