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Schr\"odinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models.
A Stochastic Approximation Method
Robbins, H. and Monro, S · 1951
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Probability Densities with Given Marginals
Kullback, S · 1968
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Reverse-time Diffusion Equation Models
Anderson, B. D · 1982
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A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
Hutchinson, M. F · 1989
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Adaptive Algorithms and Stochastic Approximations
Benveniste, A., Métivier, M., and Priouret, P · 1990
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Acceleration of Stochastic Approximation by Averaging
Polyak, B. T. and Juditsky, A · 1992
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Convergence of the Iterative Proportional Fitting Procedure
Ruschendorf, L · 1995
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A Convexity Principle for Interacting Gases
McCann, R. J · 1997
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Brownian Motion and Stochastic Calculus
Karatzas, I. and Shreve, S. E · 1998
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Statistics of Random Processes: I. General Theory
Liptser, R. S. and Shiryaev, A. N · 2001
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Introduction to Regular Perturbation Theory
Vanden-Eijnden, E · 2001
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Stochastic Differential Equations: An Introduction with Applications
Øksendal, B · 2003
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Topics in Optimal Transportation , volume 58
Villani, C · 2003
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Estimation of Non-normalized Statistical Models by Score Matching
Hyvärinen, A · 2005
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Stochastic Approximation in Monte Carlo Computation
Liang, F., Liu, C., and Carroll, R. J · 2007
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Forward-Backward Stochastic Differential Equations and their Applications
Ma, J. and Yong, J · 2007
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A Survey of the Schrödinger Problem and Some of its Connections with Optimal Transport
Léonard, C · 2014
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Stochastic Bridges of Linear Systems
Chen, Y. and Georgiou, T · 2016
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Sampling via Measure Transport: An Introduction
Marzouk, Y., Moselhy, T., Parno, M., and Spantini, A · 2016
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Variational Inference: A Review for Statisticians
Blei, D. M., Kucukelbir, A., and McAuliffe, J. D · 2017
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GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S · 2017
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Optimization for Deep Neural Networks
Trivedi, S. and Kondor, R · 2017
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FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
Grathwohl, W., Chen, R. T. Q., Bettencourt, J., Sutskever, I., and Duvenaud, D · 2019
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Computational Optimal Transport: With Applications to Data Science
Peyré, G. and Cuturi, M · 2019
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High-dimensional Multivariate Forecasting with Low-rank Gaussian Copula Processes
Salinas, D., Bohlke-Schneider, M., Callot, L., Medico, R., and Gasthaus, J · 2019
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Applied Stochastic Differential Equations
Särkkä, S. and Solin, A · 2019
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Discriminator Optimal Transport
Tanaka, A · 2019
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Refining Deep Generative Models via Discriminator Gradient Flow
Ansari, A. F., Ang, M. L., and Soh, H · 2020
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How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization
Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A · 2020
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Denoising Diffusion Probabilistic Models
Ho, J., Jain, A., and Abbeel, P · 2020
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Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form
Janati, H., Muzellec, B., Peyré, G., and Cuturi, M · 2020
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The Flow Map of the Fokker–Planck Equation Does Not Provide Optimal Transport
Lavenant, H. and Santambrogio, F · 2022
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Convergence for Score-based Generative Modeling with Polynomial Complexity
Lee, H., Lu, J., and Tan, Y · 2022
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Rectified Flow: A Marginal Preserving Approach to Optimal Transport
Liu, Q · 2022
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DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps
Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J · 2022
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Hierarchical Text-Conditional Image Generation with CLIP Latents
Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M · 2022
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Improved Techniques for Training Score-Based Generative Models
Song, Y. and Ermon, S · 2020
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Sliced Score Matching: A Scalable Approach to Density and Score Estimation
Song, Y., Garg, S., Shi, J., and Ermon, S · 2020
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Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge
Chen, Y., Georgiou, T. T., and Pavon, M · 2021
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Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling
De Bortoli, V., Thornton, J., Heng, J., and Doucet, A · 2021
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A Variational Perspective on Diffusion-Based Generative Models and Score Matching
Huang, C.-W., Lim, J. H., and Courville, A · 2021
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Kingma, D. P., Salimans, T., Poole, B., and Ho, J · 2021
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Progressive Distillation for Fast Sampling of Diffusion Models
Salimans, T. and Ho, J · 2022
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Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices, 2022
Vempala, S. S. and Wibisono, A · 2022
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Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splitting
Vono, M., Paulin, D., and Doucet, A · 2022
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Building Normalizing Flows with Stochastic Interpolants
Albergo, M. S. and Vanden-Eijnden, E · 2023
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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Albergo, M. S., Bof, N. M., and Vanden-Eijnden, E · 2023
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The Schrödinger Bridge between Gaussian Measures has a Closed Form
Bunne, C., Hsieh, Y.-P., Cuturi, m., and Krause, A · 2023
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Log-Concave Sampling
Chewi, S · 2023
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Statistical Efficiency of Score Matching: The View from Isoperimetry
Koehler, F., Heckett, A., and Risteski, A · 2023
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Flow Matching for Generative Modeling
Lipman, Y., Chen, R. T. Q., Ben-Hamu, H., Nickel, M., and Le, M · 2023
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Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
Liu, X., Gong, C., and Liu, Q · 2023
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A Comprehensive Survey on Knowledge Distillation of Diffusion Models
Luo, W · 2023
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Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling
Peluchetti, S · 2023
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Multisample Flow Matching: Straightening Flows with Minibatch Couplings
Pooladian, A.-A., Ben-Hamu, H., Domingo-Enrich, C., Amos, B., Lipman, Y., and Chen, R. T. Q · 2023
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Diffusion Schrödinger Bridge Matching
Shi, Y., De Bortoli, V., Campbell, A., and Doucet, A · 2023
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Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions
Singhal, R., Goldstein, M., and Ranganath, R · 2023
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Improving and Generalizing Flow-based Generative Models with Minibatch Optimal Transport
Tong, A., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., Fatras, K., Wolf, G., and Bengio, Y · 2023
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SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models
Xue, S., Yi, M., Luo, W., Zhang, S., Sun, J., Li, Z., and Ma, Z.-M · 2023
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Reflected Schrödinger Bridge for Constrained Generative Modeling
Deng, W., Chen, Y., Yang, N., Du, H., Feng, Q., and Chen, R. T. Q · 2024
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Enhancing Adversarial Robustness via Score-Based Optimization
Zhang, B., Luo, W., and Zhang, Z · 2024
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