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Star-Shaped Denoising Diffusion Probabilistic Models
Andrey Okhotin · Dmitry Molchanov · Arkhipkin Vladimir · Grigory Bartosh · Viktor Ohanesian · Aibek Alanov · Dmitry Vetrov

Thu Dec 14 03:00 PM -- 05:00 PM (PST) @ Great Hall & Hall B1+B2 #727

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling.Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete.In this paper, we introduce Star-Shaped DDPM (SS-DDPM).Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors.We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs.In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM.However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises–Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold.We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.Our implementation is available at https://github.com/andrey-okhotin/star-shaped

Author Information

Andrey Okhotin (Bayesian Methods Research Group Higher School of Economics)

Junior Researcher in Bayesian Methods Research Group.

Dmitry Molchanov (BayesGroup)
Arkhipkin Vladimir (Sber)
Grigory Bartosh (Higher School of Economics)
Viktor Ohanesian (Higher School of Economics, Higher School of Economics)
Aibek Alanov (Artificial Intelligence Research Institute)
Dmitry Vetrov (Higher School of Economics, AI Research Institute)

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