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This paper introduces a novel framework for designing reference diffusion processes that allows for both simulation-free training and finite-time generation in generative diffusion models. By prescribing tractable time-dependent conditional distributions, the authors demonstrate that traditional score matching is not a fundamental requirement for training these models, but rather a consequence of reversing the reference process. The findings also reveal that conditional flow matching can be derived as a small-noise limit of this new approach, providing a deeper understanding of diffusion model training dynamics.
Score matching isn't essential for diffusion model training鈥攊t's a byproduct of how we reverse the reference process.
The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.
