Andrey Okhotin

Andrey Okhotin, Dmitry Molchanov, Vladimir Arkhipkin et al.

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$\unicode{x2013}$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 .

Andrey Okhotin, Maksim Nakhodnov, Nikita Kazeev et al.

In recent years, diffusion-based models have demonstrated exceptional performance in searching for simultaneously stable, unique, and novel (S.U.N.) crystalline materials. However, most of these models don't have the ability to change the number of atoms in the crystal during the generation process, which limits the variability of model sampling trajectories. In this paper, we demonstrate the severity of this restriction and introduce a simple yet powerful technique, mirage infusion, which enables diffusion models to change the state of the atoms that make up the crystal from existent to non-existent (mirage) and vice versa. We show that this technique improves model quality by up to $\times2.5$ compared to the same model without this modification. The resulting model, Mirage Atom Diffusion (MiAD), is an equivariant joint diffusion model for de novo crystal generation that is capable of altering the number of atoms during the generation process. MiAD achieves an $8.2\%$ S.U.N. rate on the MP-20 dataset, which substantially exceeds existing state-of-the-art approaches. The source code can be found at \href{https://github.com/andrey-okhotin/miad.git}{\texttt{github.com/andrey-okhotin/miad}}.

Aleksandr Oganov, Ilya Bykov, Eva Neudachina et al.

While diffusion models achieve state-of-the-art generation quality, they still suffer from computationally expensive sampling. Recent works address this issue with gradient-based optimization methods that distill a few-step ODE diffusion solver from the full sampling process, reducing the number of function evaluations from dozens to just a few. However, these approaches often rely on intricate training techniques and do not explicitly focus on preserving fine-grained details. In this paper, we introduce the Generalized Solver: a simple parameterization of the ODE sampler that does not require additional training tricks and improves quality over existing approaches. We further combine the original distillation loss with adversarial training, which mitigates artifacts and enhances detail fidelity. We call the resulting method the Generalized Adversarial Solver and demonstrate its superior performance compared to existing solver training methods under similar resource constraints. Code is available at https://github.com/3145tttt/GAS.