Non-Denoising Forward-Time Diffusions

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the desired data distribution. We show that the time-reversal argument, common to all denoising diffusion probabilistic modeling proposals, is not necessary. We obtain diffusion processes targeting the desired data distribution by taking appropriate mixtures of diffusion bridges. The resulting transport is exact by construction, allows for greater flexibility in choosing the dynamics of the underlying diffusion, and can be approximated by means of a neural network via novel training objectives. We develop a unifying view of the drift adjustments corresponding to our and to time-reversal approaches and make use of this representation to inspect the inner workings of diffusion-based generative models. Finally, we leverage on scalable simulation and inference techniques common in spatial statistics to move beyond fully factorial distributions in the underlying diffusion dynamics. The methodological advances contained in this work contribute toward establishing a general framework for generative modeling based on diffusion processes.