mlsanityData to 14 Oct 2026

Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance

arXiv 2509.03898 ↗First posted 4 Sep 2025stat.ML cs.AI cs.LGcited by 3

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress the dataset into a latent space (from an ambient space), and train a diffusion model in the latent space; next, apply a compressed sensing algorithm to the samples generated in the latent space for decoding back to the original space; and the goal is to facilitate the efficiency of both model training and inference. Under certain sparsity assumptions on data, our proposed approach achieves provably faster convergence, via combining diffusion model inference with sparse recovery. It also sheds light on the best choice of the latent space dimension. To illustrate the effectiveness of this approach, we run numerical experiments on a range of datasets, including handwritten digits, medical and climate images, and financial time series for stress testing.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 58 of its 85 references that are in the map. First posted on arXiv 4 Sep 2025.

Builds on

58 of 85 references.

Closest ancestors · 32

Same direction, newest first

  1. 2025Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps16 Jan
  2. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
  3. 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesis11 Oct
  4. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions27 Sep
  5. 2024Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions4 Sep
  6. 2024Evaluating the design space of diffusion-based generative models18 Jun
  7. 2024Guiding a Diffusion Model with a Bad Version of Itself4 Jun
  8. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  9. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  10. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  11. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  12. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization28 Jan
20 more
  1. 2024Contractive Diffusion Probabilistic Models23 Jan
  2. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  3. 2023Improved Techniques for Training Consistency Models22 Oct
  4. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  5. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  6. 2023The probability flow ODE is provably fast19 May
  7. 2023Consistency Models2 Mar
  8. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  9. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  10. 2022Classifier-Free Diffusion Guidance26 Jul
  11. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  12. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  13. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  14. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  15. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  16. 2021Variational Diffusion Models1 Jul
  17. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  18. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  19. 2020Denoising Diffusion Implicit Models6 Oct
  20. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 26

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,742
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  7. 2023Training Diffusion Models with Reinforcement Learningcited by 982
  8. 2025Large Language Diffusion Modelscited by 912
  9. 2021MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classificationcited by 690
  10. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 450
  11. 2017Compressed Sensing using Generative Modelscited by 339
  12. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
14 more
  1. 2025Mercury: Ultra-Fast Language Models Based on Diffusioncited by 235
  2. 2018Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholdscited by 85
  3. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  4. 2015From error bounds to the complexity of first-order descent methods for convex functionscited by 43
  5. 2025Score as Action: Fine-Tuning Diffusion Generative Models by Continuous-time Reinforcement Learningcited by 33
  6. 2024Preference Tuning with Human Feedback on Language, Speech, and Vision Tasks: A Surveycited by 23
  7. 2025Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structurecited by 13
  8. 2020Iteratively Reweighted Least Squares for Basis Pursuit with Global Linear Convergence Ratecited by 10
  9. 2015Local Linear Convergence of ISTA and FISTA on the LASSO Problemcited by 8
  10. 2023A Survey of Numerical Algorithms that can Solve the Lasso Problemscited by 5
  11. 2025Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion modelcited by 5
  12. 2015Local and Global Convergence of an Inertial Version of Forward-Backward Splittingcited by 1
  13. 2019Restart FISTA with Global Linear Convergencecited by 1
  14. 2025Data-Driven Dynamic Factor Modeling via Manifold Learningcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approachcited by 11
  2. 2026Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Trainingcited by 3
  3. 2026Tweedie's Formulae and Diffusion Generative Models Beyond Gaussiancited by 0

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