Hessian Geometry of Latent Space in Generative Models

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.

Training-Free Voice Conversion with Factorized Optimal Transport

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.

Color Transfer with Modulated Flows

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

Color Conditional Generation with Sliced Wasserstein Guidance

We propose SW-Guidance, a training-free approach for image generation conditioned on the color distribution of a reference image. While it is possible to generate an image with fixed colors by first creating an image from a text prompt and then applying a color style transfer method, this approach often results in semantically meaningless colors in the generated image. Our method solves this problem by modifying the sampling process of a diffusion model to incorporate the differentiable Sliced 1-Wasserstein distance between the color distribution of the generated image and the reference palette. Our method outperforms state-of-the-art techniques for color-conditional generation in terms of color similarity to the reference, producing images that not only match the reference colors but also maintain semantic coherence with the original text prompt. Our source code is available at https://github.com/alobashev/sw-guidance/.