Dmitry Guskov

Maria Larchenko, Alexander Lobashev, Dmitry Guskov et al.

In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for new images. After training on a set of optimal transport plans, our approach can generate plans for new pairs of distributions without additional fine-tuning. We additionally show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity. Our source code is available at https://github.com/maria-larchenko/modflows

Alexander Lobashev, Dmitry Guskov, Maria Larchenko et al.

This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the posterior distribution of latent variables given generated samples and uses this to learn the log-partition function, which defines the Fisher metric for exponential families. Theoretical convergence guarantees are provided, and the method is validated on the Ising and TASEP models, outperforming existing baselines in reconstructing thermodynamic quantities. Applied to diffusion models, the method reveals a fractal structure of phase transitions in the latent space, characterized by abrupt changes in the Fisher metric. We demonstrate that while geodesic interpolations are approximately linear within individual phases, this linearity breaks down at phase boundaries, where the diffusion model exhibits a divergent Lipschitz constant with respect to the latent space. These findings provide new insights into the complex structure of diffusion model latent spaces and their connection to phenomena like phase transitions. Our source code is available at https://github.com/alobashev/hessian-geometry-of-diffusion-models.

Alexander Lobashev, Dmitry Guskov, Kirill Polovnikov

Fractional Brownian motion (fBm) features both randomness and strong scale-free correlations, challenging generative models to reproduce the intrinsic memory characterizing the underlying stochastic process. Here we examine a zoo of diffusion-based inpainting methods on a specific dataset of corrupted images, which represent incomplete Euclidean distance matrices (EDMs) of fBm at various memory exponents $H$. Our dataset implies uniqueness of the data imputation in the regime of low missing ratio, where the remaining partial graph is rigid, providing the ground truth for the inpainting. We find that the conditional diffusion generation readily reproduces the built-in correlations of fBm paths in different memory regimes (i.e., for sub-, Brownian and super-diffusion trajectories), providing a robust tool for the statistical imputation at high missing ratio. Furthermore, while diffusion models have been recently shown to memorize samples from the training database, we demonstrate that diffusion behaves qualitatively different from the database search and thus generalize rather than memorize the training dataset. As a biological application, we apply our fBm-trained diffusion model for the imputation of microscopy-derived distance matrices of chromosomal segments (FISH data) - incomplete due to experimental imperfections - and demonstrate its superiority over the standard approaches used in bioinformatics.