Toward a Unified Framework for Consistency Generative Modeling

Consistency modeling, a novel generative paradigm inspired by diffusion models, has gained traction for its capacity to facilitate real-time generation through single-step sampling. While its advantages are evident, the understanding of its underlying principles and effective algorithmic enhancements remains elusive. In response, we present a unified framework for consistency generative modeling, without resorting to the predefined diffusion process. Instead, it directly constructs a probability density path that bridges the two distributions. Building upon this novel perspective, we introduce a more general consistency training objective that encapsulates previous consistency models and paves the way for innovative, consistency generation techniques. In particular, we introduce two novel models: Poisson consistency models (PCMs) and coupling consistency models (CCMs), which extend the prior distribution of latent variables beyond the Gaussian form. This extension significantly augments the flexibility of generative modeling. Furthermore, we harness the principles of optimal transport (OT) to mitigate variance during consistency training, substantially improving convergence and generative quality. Extensive experiments on the generation of synthetic and real-world datasets, as well as image-to-image translation tasks (I2I), demonstrate the effectiveness of the proposed approaches.