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.

This paper presents a new method for finding the optimal positions for sensors used to reconstruct geophysical fields from sparse measurements. The method is composed of two stages. In the first stage, we estimate the spatial variability of the physical field by approximating its information entropy using the Conditional Pixel CNN network. In the second stage, the entropy is used to initialize the distribution of optimal sensor locations, which is then optimized using the Concrete Autoencoder architecture with the straight-through gradient estimator for the binary mask and with adversarial loss. This allows us to simultaneously minimize the number of sensors and maximize reconstruction accuracy. We apply our method to the global ocean under-surface temperature field and demonstrate its effectiveness on fields with up to a million grid cells. Additionally, we find that the information entropy field has a clear physical interpretation related to the mixing between cold and warm currents.

In this paper, effects of low and high ambient temperatures on the operation of a photoelectric unit are investigated. The research methodology consisted in determination of the energy efficiency of a photoelectric unit across a wide range of ambient temperatures, providing graphical interpretations and describing the procedure of field observations. Regularities in determining the average statistical indicators of energy efficiency rise and drop in a photoelectric unit were applied for a particular range of ambient temperatures. These studies were undertaken during the winter of 2021 in the Materials Science Laboratory of V.P. Larionov Institute of Physical-Technical Problems of the North, Siberian Branch of the Russian Academy of Sciences, using a fixed climate chamber. Reference parameters were obtained for changes in the photoelectric unit generating capacity (within -60ºC to +60ºC), which can be applied in modeling operational processes and engineering calculations of operating conditions of solar power plants. It was found that, at the same illumination and ambient temperature values, a photoelectric panel generates the maximum energy at -60ºC and minimal energy at +60 ºC, with the specific power drop for this temperature range being 19%. A significant drop in the specific power of the photoelectric unit was achieved at +30 ºC and higher due to the increased internal resistance of the unit. For temperatures below -40ºC, the specific power of the analyzed unit increased insignificantly due to the decreased internal resistance of the unit. The obtained values of the generating capacity of a photoelectric unit within a wide range of ambient temperatures can be used in developing a procedure for evaluating the effects of ambient temperature and its various ranges on the operation of photoelectric units, as well as for a more accurate determination of the solar generation energy potential under certain climate conditions. In future studies, field observations are planned to identify the nature of the effect of two and more climatic factors on the operation of a photoelectric unit.

The paper examines the impact of sensor placement on the accuracy of the Global ocean state forecasting. A comparison is made between various sensor placement methods, including the arrangement obtained by the Concrete Autoencoder method. To evaluate how sensor placement affects forecast accuracy, a simulation was conducted that emulates a scenario where the initial state of the global ocean significantly deviates from the ground truth. In the experiment, initial conditions for the ocean and ice model were altered, while atmospheric forcing was retained from the control experiment. Subsequently, the model was integrated with the assimilation of data about the ground truth state at the sensor locations. The results showed that the sensor placement obtained using deep learning methods is superior in forecast accuracy to other considered arrays with a comparable number of sensors.

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.

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.