Data to 7 Oct 2026

Theoretical guarantees for sampling and inference in generative models with latent diffusions

arXiv 1903.01608 ↗First posted 5 Mar 2019math.PR cs.LG math.OCcited by 97

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Cited by 41 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: We provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. We quantify the expressiveness of diffusion-based generative models. Specifically, we show that one can efficiently sample from a wide class of terminal target distributions by choosing the drift of the latent diffusion from the class of multilayer feedforward neural nets, with the accuracy of sampling measured by the Kullback-Leibler divergence to the target distribution. Finally, we present and analyze a scheme for unbiased simulation of generative models with latent diffusions and provide bounds on the variance of the resulting estimators. This scheme can be implemented as a deep generative model with a random number of layers.

Key facts. Cited by 97 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Mar 2019.

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Citing papers per year: 2021: 10; 2022: 10; 2023: 16; 2024: 26; 2025: 20; 2026: 15.

97 papers.

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2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
2022Convergence for score-based generative modeling with polynomial complexitycited by 176
2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
2024Semantic Image Inversion and Editing using Rectified Stochastic Differential Equationscited by 162
2021Neural SDEs as Infinite-Dimensional GANscited by 159
2022An optimal control perspective on diffusion-based generative modelingcited by 145
2023Denoising Diffusion Samplerscited by 144
2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 136
2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113

38 more

2023Improved sampling via learned diffusionscited by 103
2022Let us Build Bridges: Understanding and Extending Diffusion Generative Modelscited by 102
2023Efficient Dataset Distillation via Minimax Diffusioncited by 81
2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
2021Efficient and Accurate Gradients for Neural SDEscited by 68
2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 61
2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 61
2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
2022Fast Point Cloud Generation with Straight Flowscited by 56
2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 52
2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
2024Improved off-policy training of diffusion samplerscited by 47
2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
2023Reverse Diffusion Monte Carlocited by 41
2022Normalizing flow neural networks by JKO schemecited by 39
2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
2024Stochastic Localization via Iterative Posterior Samplingcited by 27
2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 22
2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 17
2023Latent SDEs on Homogeneous Spacescited by 16
2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
2023Neural Structure Learning with Stochastic Differential Equationscited by 14
2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11
2024Harmonic Path Integral Diffusioncited by 11
2025HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimizationcited by 10
2022Fractional SDE-Net: Generation of Time Series Data with Long-term Memorycited by 9
2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
2024Soft-constrained Schrodinger Bridge: a Stochastic Control Approachcited by 8
2021Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexitycited by 7

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