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Alexander Filippov

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3 papers

2 author rows

ICLR Conference 2025 Conference Paper

A3D: Does Diffusion Dream about 3D Alignment?

Savva Victorovich Ignatyev
Nina Konovalova
Daniil Selikhanovych
Oleg Voynov
Nikolay Patakin
Ilya Olkov
Dmitry Senushkin
Alexey Artemov

We tackle the problem of text-driven 3D generation from a geometry alignment perspective. Given a set of text prompts, we aim to generate a collection of objects with semantically corresponding parts aligned across them. Recent methods based on Score Distillation have succeeded in distilling the knowledge from 2D diffusion models to high-quality representations of the 3D objects. These methods handle multiple text queries separately, and therefore the resulting objects have a high variability in object pose and structure. However, in some applications, such as 3D asset design, it may be desirable to obtain a set of objects aligned with each other. In order to achieve the alignment of the corresponding parts of the generated objects, we propose to embed these objects into a common latent space and optimize the continuous transitions between these objects. We enforce two kinds of properties of these transitions: smoothness of the transition and plausibility of the intermediate objects along the transition. We demonstrate that both of these properties are essential for good alignment. We provide several practical scenarios that benefit from alignment between the objects, including 3D editing and object hybridization, and experimentally demonstrate the effectiveness of our method.

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NeurIPS Conference 2021 Conference Paper

Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark

Alexander Korotin
Lingxiao Li
Aude Genevay
Justin M. Solomon
Alexander Filippov
Evgeny Burnaev

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport---specifically, computation of the Wasserstein-2 distance, a commonly-used formulation of optimal transport in machine learning. To overcome the challenge of computing ground truth transport maps between continuous measures needed to assess these solvers, we use input-convex neural networks (ICNN) to construct pairs of measures whose ground truth OT maps can be obtained analytically. This strategy yields pairs of continuous benchmark measures in high-dimensional spaces such as spaces of images. We thoroughly evaluate existing optimal transport solvers using these benchmark measures. Even though these solvers perform well in downstream tasks, many do not faithfully recover optimal transport maps. To investigate the cause of this discrepancy, we further test the solvers in a setting of image generation. Our study reveals crucial limitations of existing solvers and shows that increased OT accuracy does not necessarily correlate to better results downstream.

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NeurIPS Conference 2021 Conference Paper

Manifold Topology Divergence: a Framework for Comparing Data Manifolds.

Serguei Barannikov
Ilya Trofimov
Grigorii Sotnikov
Ekaterina Trimbach
Alexander Korotin
Alexander Filippov
Evgeny Burnaev

We propose a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P, Q), that, given a pair of distributions in a high-dimensional space, tracks multiscale topology spacial discrepancies between manifolds on which the distributions are concentrated. Based on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it to assess the performance of deep generative models in various domains: images, 3D-shapes, time-series, and on different datasets: MNIST, Fashion MNIST, SVHN, CIFAR10, FFHQ, market stock data, ShapeNet. We demonstrate that the MTop-Divergence accurately detects various degrees of mode-dropping, intra-mode collapse, mode invention, and image disturbance. Our algorithm scales well (essentially linearly) with the increase of the dimension of the ambient high-dimensional space. It is one of the first TDA-based methodologies that can be applied universally to datasets of different sizes and dimensions, including the ones on which the most recent GANs in the visual domain are trained. The proposed method is domain agnostic and does not rely on pre-trained networks.

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