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Whereas diverse variations of diffusion models exist, extending the linear diffusion into a nonlinear diffusion process is investigated by very few works.
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A computational fluid mechanics solution to the monge-kantorovich mass transfer problem
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An algorithmic introduction to numerical simulation of stochastic differential equations
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Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Optimal transport: old and new , volume 338
Cédric Villani · 2009
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Hilbert space embeddings and metrics on probability measures
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Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
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Stochastic differential equations: an introduction with applications
Bernt Oksendal · 2013
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Topology and geometry , volume 139
Glen E Bredon · 2013
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Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2014
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Variational inference with normalizing flows
Danilo Rezende and Shakir Mohamed · 2015
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U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
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Lecture notes for statistics 311/electrical engineering 377
John Duchi · 2016
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On the relation between optimal transport and schrödinger bridges: A stochastic control viewpoint
Yongxin Chen, Tryphon T Georgiou, and Michele Pavon · 2016
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Pixel recurrent neural networks
Aaron Van Oord, Nal Kalchbrenner, and Koray Kavukcuoglu · 2016
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Searching for activation functions
Prajit Ramachandran, Barret Zoph, and Quoc V Le · 2017
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Image transformer
Niki Parmar, Ashish Vaswani, Jakob Uszkoreit, Lukasz Kaiser, Noam Shazeer, Alexander Ku, and Dustin Tran · 2018
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Glow: Generative flow with invertible 1x1 convolutions
Durk P Kingma and Prafulla Dhariwal · 2018
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Preventing posterior collapse with delta-vaes
Ali Razavi, Aaron van den Oord, Ben Poole, and Oriol Vinyals · 2018
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A style-based generator architecture for generative adversarial networks
Tero Karras, Samuli Laine, and Timo Aila · 2019
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Residual flows for invertible generative modeling
Ricky TQ Chen, Jens Behrmann, David K Duvenaud, and Jörn-Henrik Jacobsen · 2019
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Flow++: Improving flow-based generative models with variational dequantization and architecture design
Jonathan Ho, Xi Chen, Aravind Srinivas, Yan Duan, and Pieter Abbeel · 2019
A variational perspective on diffusion-based generative models and score matching
Chin-Wei Huang, Jae Hyun Lim, and Aaron C Courville · 2021
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Diffusion normalizing flow
Qinsheng Zhang and Yongxin Chen · 2021
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Solving schrödinger bridges via maximum likelihood
Francisco Vargas, Pierre Thodoroff, Austen Lamacraft, and Neil Lawrence · 2021
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Diffusion schrödinger bridge with applications to score-based generative modeling
Valentin De Bortoli, James Thornton, Jeremy Heng, and Arnaud Doucet · 2021
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Hopf–cole transformation via generalized schrödinger bridge problem
Flavien Léger and Wuchen Li · 2021
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Decoupling global and local representations via invertible generative flows
Xuezhe Ma, Xiang Kong, Shanghang Zhang, and Eduard H Hovy · 2021
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Applied stochastic differential equations , volume 10
Simo Särkkä and Arno Solin · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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Generating long sequences with sparse transformers
Rewon Child, Scott Gray, Alec Radford, and Ilya Sutskever · 2019
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Nvae: A deep hierarchical variational autoencoder
Arash Vahdat and Jan Kautz · 2020
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Improved techniques for training score-based generative models
Yang Song and Stefano Ermon · 2020
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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Variational diffusion models
Diederik P Kingma, Tim Salimans, Ben Poole, and Jonathan Ho · 2021
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Non gaussian denoising diffusion models
Eliya Nachmani, Robin San Roman, and Lior Wolf · 2021
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Consistency regularization for variational auto-encoders
Samarth Sinha and Adji Bousso Dieng · 2021
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Palette: Image-to-image diffusion models
Chitwan Saharia, William Chan, Huiwen Chang, Chris A. Lee, Jonathan Ho, Tim Salimans, David J. Fleet, and Mohammad Norouzi · 2021
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Unit-ddpm: Unpaired image translation with denoising diffusion probabilistic models
Hiroshi Sasaki, Chris G Willcocks, and Toby P Breckon · 2021
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Pot: Python optimal transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
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Implicit normalizing flows
Cheng Lu, Jianfei Chen, Chongxuan Li, Qiuhao Wang, and Jun Zhu · 2021
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Improved denoising diffusion probabilistic models
Alexander Quinn Nichol and Prafulla Dhariwal · 2021
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Transgan: Two pure transformers can make one strong gan, and that can scale up
Yifan Jiang, Shiyu Chang, and Zhangyang Wang · 2021
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Dual contradistinctive generative autoencoder
Gaurav Parmar, Dacheng Li, Kwonjoon Lee, and Zhuowen Tu · 2021
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Likelihood training of schrödinger bridge using forward-backward SDEs theory
Tianrong Chen, Guan-Horng Liu, and Evangelos Theodorou · 2022
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Score-based generative modeling with critically-damped langevin diffusion
Tim Dockhorn, Arash Vahdat, and Karsten Kreis · 2022
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Wavelet score-based generative modeling
Florentin Guth, Simon Coste, Valentin De Bortoli, and Stephane Mallat · 2022
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Soft truncation: A universal training technique of score-based diffusion model for high precision score estimation
Dongjun Kim, Seungjae Shin, Kyungwoo Song, Wanmo Kang, and Il-Chul Moon · 2022
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Louay Hazami, Rayhane Mama, and Ragavan Thurairatnam · 2022
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Understanding ddpm latent codes through optimal transport
Valentin Khrulkov and Ivan Oseledets · 2022
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On aliased resizing and surprising subtleties in gan evaluation, 2022
Gaurav Parmar, Richard Zhang, and Jun-Yan Zhu · 2022
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Convergence of denoising diffusion models under the manifold hypothesis
Valentin De Bortoli · 2022
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Styleformer: Transformer based generative adversarial networks with style vector
Jeeseung Park and Younggeun Kim · 2022
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