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.
M. A. Larchenko, R. R. Zagidullin, V. V. Palyulin et al.
Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of particle propagation. Low rank approximation for the aggregation kernels can significantly speed up the solution of Smoluchowski equations, while particle propagation could be done in parallel. Yet the simulations with many aggregate sizes remain quite resource-demanding. Here, we explore the way to reduce the amount of direct computations with the use of modern machine learning (ML) techniques. Namely, we propose to replace the actual numerical solution of the Smoluchowki equations with the respective density transformations learned with the application of the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution requires drastically less computation time and agrees fairly well with the results of direct numerical simulations. Such an opportunity of a quick forecast of space-dependent particle size distribution could be important in practice, especially for the online prediction and visualisation of pollution processes, providing a tool with a reasonable tradeoff between the prediction accuracy and the computational time.
Maria Larchenko, Dmitry Guskov, Alexander Lobashev et al.
Color harmonization adjusts the colors of an inserted object so that it perceptually matches the surrounding image, resulting in a seamless composite. The harmonization problem naturally arises in augmented reality (AR), yet harmonization algorithms are not currently integrated into AR pipelines because real-time solutions are scarce. In this work, we address color harmonization for AR by proposing a lightweight approach that supports on-device inference. For this, we leverage classical optimal transport theory by training a compact encoder to predict the Monge-Kantorovich transport map. We benchmark our MKL-Harmonizer algorithm against state-of-the-art methods and demonstrate that for real composite AR images our method achieves the best aggregated score. We release our dedicated AR dataset of composite images with pixel-accurate masks and data-gathering toolkit to support further data acquisition by researchers.
Alexander Lobashev, Assel Yermekova, Maria Larchenko
This paper introduces Factorized MKL-VC, a training-free modification for kNN-VC pipeline. In contrast with original pipeline, our algorithm performs high quality any-to-any cross-lingual voice conversion with only 5 second of reference audio. MKL-VC replaces kNN regression with a factorized optimal transport map in WavLM embedding subspaces, derived from Monge-Kantorovich Linear solution. Factorization addresses non-uniform variance across dimensions, ensuring effective feature transformation. Experiments on LibriSpeech and FLEURS datasets show MKL-VC significantly improves content preservation and robustness with short reference audio, outperforming kNN-VC. MKL-VC achieves performance comparable to FACodec, especially in cross-lingual voice conversion domain.
Optimization of first-passage times is required in applications ranging from nanobots navigation to market trading. In such settings, one often encounters unevenly distributed noise levels across the environment. We extensively study how a learning agent fares in 1- and 2- dimensional heated gridworlds with an uneven temperature distribution. The results show certain bias effects in agents trained via simple tabular Q-learning, SARSA, Expected SARSA and Double Q-learning. While high learning rate prevents exploration of regions with higher temperature, low enough rate increases the presence of agents in such regions. The discovered peculiarities and biases of temporal-difference-based reinforcement learning methods should be taken into account in real-world physical applications and agent design.