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Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling [article]

Valentin De Bortoli, James Thornton, Jeremy Heng, Arnaud Doucet
2021 arXiv   pre-print
We present Diffusion SB (DSB), an original approximation of the Iterative Proportional Fitting (IPF) procedure to solve the SB problem, and provide theoretical analysis along with generative modeling experiments  ...  In contrast, solving the Schr\"odinger Bridge problem (SB), i.e. an entropy-regularized optimal transport problem on path spaces, yields diffusions which generate samples from the data distribution in  ...  Discussion Score-based generative modeling (SGM) may be viewed as the first stage of solving a Schrödinger bridge problem.  ... 
arXiv:2106.01357v4 fatcat:vmvu7hicpbd7hjxqdgvr7bhqji

Riemannian Diffusion Schrödinger Bridge [article]

James Thornton, Michael Hutchinson, Emile Mathieu, Valentin De Bortoli, Yee Whye Teh, Arnaud Doucet
2022 arXiv   pre-print
Our proposed method generalizes Diffusion Schrödinger Bridge introduced in to the non-Euclidean setting and extends Riemannian score-based models beyond the first time reversal.  ...  To overcome these issues, we introduce Riemannian Diffusion Schrödinger Bridge.  ...  Background 1.Score Based Generative Modeling In Euclidean spaces, Score-based Generative Modeling (SGM) (Song & Ermon, 2019; Song et al., 2021b ) consists of two main components.  ... 
arXiv:2207.03024v1 fatcat:rdeza3l6ynbyzje7tvqctrgny4

Dual Diffusion Implicit Bridges for Image-to-Image Translation [article]

Xuan Su, Jiaming Song, Chenlin Meng, Stefano Ermon
2022 arXiv   pre-print
We present Dual Diffusion Implicit Bridges (DDIBs), an image translation method based on diffusion models, that circumvents training on domain pairs.  ...  Image translation with DDIBs relies on two diffusion models trained independently on each domain, and is a two-step process: DDIBs first obtain latent encodings for source images with the source diffusion  ...  Schrödinger Bridge for Generative Modeling Solutions to the SBP (Section 2) are commonly used to design generative models.  ... 
arXiv:2203.08382v2 fatcat:so2y265i7rbatfhgqyxjgwra7e

Solving Schrödinger Bridges via Maximum Likelihood

Francisco Vargas, Pierre Thodoroff, Austen Lamacraft, Neil Lawrence
2021 Entropy  
Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research.  ...  The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution.  ...  Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling. arXiv2021, arXiv:2106.01357. [Google Scholar] Feydy, J. Geometric Data Analysis, beyond Convolutions.  ... 
doi:10.3390/e23091134 pmid:34573759 pmcid:PMC8464739 fatcat:73ndpz6pjzdpzpk2wtroqzcok4

Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory [article]

Tianrong Chen, Guan-Horng Liu, Evangelos A. Theodorou
2022 arXiv   pre-print
Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based  ...  on the suitability of SB models as a principled alternative for generative applications.  ...  ACKNOWLEDGMENTS The authors would like to thank Ioannis Exarchos and Oswin So for their generous involvement and helpful supports during the rebuttal.  ... 
arXiv:2110.11291v4 fatcat:7qibgjbbuvbb5aghaujhu7lei4

Applying Regularized Schrödinger-Bridge-Based Stochastic Process in Generative Modeling [article]

Ki-Ung Song
2022 arXiv   pre-print
Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach.  ...  Schr\"odinger bridge (SB)-based models attempt to tackle this problem by training bidirectional stochastic processes between distributions.  ...  Conclusion This study tried to utilize bidirectional stochastic processes based on the Schrödinger bridge (SB) problem for deep generative modeling.  ... 
arXiv:2208.07131v1 fatcat:ixfp4g5tbvexha6ek2z72lbtji

Solving Schrödinger Bridges via Maximum Likelihood [article]

Francisco Vargas, Pierre Thodoroff, Neil D. Lawrence, Austen Lamacraft
2021 arXiv   pre-print
Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schr\"odinger bridge remain an active area of research.  ...  As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing.  ...  Diffusion schr\" odinger bridge with applications to score-based generative modeling. arXiv preprint arXiv:2106.01357. [Elliott and Anderson 1985] Elliott, R. J., and Anderson, B. D. 1985.  ... 
arXiv:2106.02081v6 fatcat:yu6j3rrl4ndifopn5jlven5weq

Diffusion-based Molecule Generation with Informative Prior Bridges [article]

Lemeng Wu, Chengyue Gong, Xingchao Liu, Mao Ye, Qiang Liu
2022 arXiv   pre-print
We propose a simple and novel approach to steer the training of diffusion-based generative models with physical and statistics prior information.  ...  With comprehensive experiments, we show that our method provides a powerful approach to the 3D generation task, yielding molecule structures with better quality and stability scores and more uniformly  ...  We would like to thank the anonymous reviewers and the area chair for their thoughtful comments and efforts towards improving our manuscript.  ... 
arXiv:2209.00865v1 fatcat:a5yszg6oibblzb6fo2qrankkwu

Deep Generative Learning via Schrödinger Bridge [article]

Gefei Wang, Yuling Jiao, Qian Xu, Yang Wang, Can Yang
2021 arXiv   pre-print
We propose to learn a generative model via entropy interpolation with a Schrödinger Bridge.  ...  Experimental results on multimodal synthetic data and benchmark data support our theoretical findings and indicate that the generative model via Schrödinger Bridge is comparable with state-of-the-art GANs  ...  To fill the gap, we propose a Schrödinger Bridge approach to learn generative models.  ... 
arXiv:2106.10410v2 fatcat:domn5aacezb57ay2ppmpi6s5xq

First Hitting Diffusion Models [article]

Mao Ye, Lemeng Wu, Qiang Liu
2022 arXiv   pre-print
We propose a family of First Hitting Diffusion Models (FHDM), deep generative models that generate data with a diffusion process that terminates at a random first hitting time.  ...  Technically, we train FHDM by maximum likelihood estimation on diffusion trajectories augmented from observed data with conditional first hitting processes (i.e., bridge) derived based on Doob's h-transform  ...  Schrodinger bridges is an another well studied framework of diffusion model [46, 11, 34, 10] . However, using Schrodinger bridges usually require expensive forward-backward algorithms.  ... 
arXiv:2209.01170v1 fatcat:dszcbayly5bxlhnz5stzcedkw4

Elucidating Binding Sites and Affinities of ERα Agonists and Antagonists to Human Alpha-Fetoprotein by In Silico Modeling and Point Mutagenesis

Nurbubu T. Moldogazieva, Daria S. Ostroverkhova, Nikolai N. Kuzmich, Vladimir V. Kadochnikov, Alexander A. Terentiev, Yuri B. Porozov
2020 International Journal of Molecular Sciences  
Based on the ligand-docked scoring functions, we identified three putative estrogen- and antiestrogen-binding sites with different ligand binding affinities.  ...  In our study, we constructed a homology-based 3D model of human AFP (HAFP) with the purpose of molecular docking of ERα ligands, three agonists (17β-estradiol, estrone and diethylstilbestrol), and three  ...  LigPrep suite [61] in Schrödinger software with application of the OPLS3e force field.  ... 
doi:10.3390/ijms21030893 pmid:32019136 pmcid:PMC7036865 fatcat:ww26eltq6zewfnfciyns4igdqy

Conditional Simulation Using Diffusion Schrödinger Bridges [article]

Yuyang Shi, Valentin De Bortoli, George Deligiannidis, Arnaud Doucet
2022 arXiv   pre-print
Denoising diffusion models have recently emerged as a powerful class of generative models.  ...  When performing unconditional simulation, a Schr\"odinger bridge formulation of generative modeling leads to a theoretically grounded algorithm shortening generation time which is complementary to other  ...  We are also grateful to the authors of [Kovachki et al., 2021] for sharing their code with us.  ... 
arXiv:2202.13460v2 fatcat:c2tlq7f72ff6lfn4uz4qanakzq

On local entropy, stochastic control and deep neural networks [article]

Michele Pavon
2022 arXiv   pre-print
In this paper, we connect some recent papers on smoothing of energy landscapes and scored-based generative models of machine learning to classical work in stochastic control.  ...  We clarify these connections providing rigorous statements and representations which may serve as guidelines for further learning models.  ...  The corresponding optimal control, see (22) below, is then related to the socalled score-function ∇ log p(x, t) of generative models of machine learning based on flows [1] , [33] , [14] , [22] ,  ... 
arXiv:2204.13049v2 fatcat:zt7wp4hbgrgitobiuu4gb6p27u

Diffusion Models: A Comprehensive Survey of Methods and Applications [article]

Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Yingxia Shao, Wentao Zhang, Bin Cui, Ming-Hsuan Yang
2022 arXiv   pre-print
Diffusion models are a class of deep generative models that have shown impressive results on various tasks with a solid theoretical foundation.  ...  Furthermore, we propose new perspectives pertaining to the development of generative models. Github:  ...  Grad-TTS [165] presents a novel text-to-speech model with a score-based decoder and diffusion models.  ... 
arXiv:2209.00796v7 fatcat:3xzsrolirfhu5m4uy42l7dfcmi

Simulating Diffusion Bridges with Score Matching [article]

Valentin De Bortoli, Arnaud Doucet, Jeremy Heng, James Thornton
2021 arXiv   pre-print
As our approach is generally applicable under mild assumptions on the underlying diffusion process, it can easily be used to improve the proposal bridge process within existing methods and frameworks.  ...  Diffusion bridge simulation has applications in diverse scientific fields and plays a crucial role for statistical inference of discretely-observed diffusions.  ...  As our approach is generally applicable under mild assumptions on the SDE in (1), it can easily be used to improve the proposal bridge process within existing methods and frameworks.  ... 
arXiv:2111.07243v1 fatcat:ubtfb6x27veb7lm46pl2y7hddm
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