Go With the Flow: Fast Diffusion for Gaussian Mixture Models
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| Gepubliceerd in: | arXiv.org (Dec 24, 2024), p. n/a |
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| Hoofdauteur: | |
| Andere auteurs: | , |
| Gepubliceerd in: |
Cornell University Library, arXiv.org
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| Onderwerpen: | |
| Online toegang: | Citation/Abstract Full text outside of ProQuest |
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| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 3144197775 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 3144197775 | ||
| 045 | 0 | |b d20241224 | |
| 100 | 1 | |a Rapakoulias, George | |
| 245 | 1 | |a Go With the Flow: Fast Diffusion for Gaussian Mixture Models | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 24, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a Schr\"{o}dinger Bridges (SB) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been proposed in the literature, most of these approaches require computationally expensive training schemes, even for solving low-dimensional problems. In this work, we propose an analytic parametrization of a set of feasible policies for steering the distribution of a dynamical system from one Gaussian Mixture Model (GMM) to another. Instead of relying on standard non-convex optimization techniques, the optimal policy within the set can be approximated as the solution of a low-dimensional linear program whose dimension scales linearly with the number of components in each mixture. Furthermore, our method generalizes naturally to more general classes of dynamical systems such as controllable Linear Time-Varying systems that cannot currently be solved using traditional neural SB approaches. We showcase the potential of this approach in low-to-moderate dimensional problems such as image-to-image translation in the latent space of an autoencoder, and various other examples. We also benchmark our approach on an Entropic Optimal Transport (EOT) problem and show that it outperforms state-of-the-art methods in cases where the boundary distributions are mixture models while requiring virtually no training. | |
| 653 | |a Probabilistic models | ||
| 653 | |a Diffusion rate | ||
| 653 | |a Parameterization | ||
| 653 | |a Controllability | ||
| 653 | |a Dynamical systems | ||
| 653 | |a Convexity | ||
| 653 | |a Time varying control systems | ||
| 653 | |a Dimensional analysis | ||
| 653 | |a Optimization techniques | ||
| 653 | |a Normal distribution | ||
| 653 | |a Optimization | ||
| 700 | 1 | |a Pedram, Ali Reza | |
| 700 | 1 | |a Tsiotras, Panagiotis | |
| 773 | 0 | |t arXiv.org |g (Dec 24, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3144197775/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2412.09059 |