Non-Denoising Forward-Time Diffusions

By Stefano Peluchetti. 2023

102 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Flow Matching for Generative Modeling (2022, neutral): “In an another line of works, (De Bortoli et al., 2021; Wang et al., 2021; Peluchetti, 2021) proposed finite time diffusion constructions via diffusion bridges theory resolving the approximation error incurred by infinite time denoising constructions.”
Improving and generalizing flow-based generative models with minibatch optimal transport (2023, unknown): “In Table 3 we compare SB-CFM and the diffusion Schr¨odinger bridge (DSB) method introduced in De Bortoli et al. (2021) on the quality of the learnt Schr¨odinger bridges based on the average 2-Wasserstein distance to ground truth Schr¨odinger bridge samples over 18 time steps.”
Building Normalizing Flows with Stochastic Interpolants (2022, unknown): “Similarly, Peluchetti (2022) investigates the use of bridge processes, i.e. SDE whose position is constrained both at the initial and ﬁnal times, to perform exact density interpolation in ﬁnite time.”
SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers (2024, background): “Finally, various work considers learning a stochastic bridge connecting two arbitrary distributions [18, 41, 49, 56].”