mlsanityData to 14 Oct 2026

Implicit Diffusion: Efficient Optimization through Stochastic Sampling

arXiv 2402.05468 ↗First posted 8 Feb 2024cs.LGcited by 24

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Abstract (arXiv)

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness. We apply it to training energy-based models and finetuning denoising diffusions.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). Builds on 52 of its 99 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

52 of 99 references.

References · 52

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  5. 2022Scalable Diffusion Models with Transformerscited by 6,054
  6. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  7. 2022Prompt-to-Prompt Image Editing with Cross Attention Controlcited by 2,431
  8. 2019Fine-Tuning Language Models from Human Preferencescited by 2,150
  9. 2018DARTS: Differentiable Architecture Searchcited by 1,798
  10. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  11. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  12. 2023Training Diffusion Models with Reinforcement Learningcited by 982
38 more
  1. 2023RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignmentcited by 686
  2. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  3. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 450
  4. 2023Directly Fine-Tuning Diffusion Models on Differentiable Rewardscited by 448
  5. 2023Simple diffusion: End-to-end diffusion for high resolution imagescited by 422
  6. 2023Aligning Text-to-Image Models using Human Feedbackcited by 422
  7. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 405
  8. 2022Diffusion Models already have a Semantic Latent Spacecited by 328
  9. 2023Human Preference Score: Better Aligning Text-to-Image Models with Human Preferencecited by 287
  10. 2022On Neural Differential Equationscited by 268
  11. 2016Hyperparameter optimization with approximate gradientcited by 233
  12. 2022Diffusion models as plug-and-play priorscited by 231
  13. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  14. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  15. 2021Efficient and Modular Implicit Differentiationcited by 203
  16. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Qualitycited by 182
  17. 2020A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Criticcited by 144
  18. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
  19. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  20. 2022Uncovering the Disentanglement Capability in Text-to-Image Diffusion Modelscited by 116
  21. 2023End-to-End Diffusion Latent Optimization Improves Classifier Guidancecited by 108
  22. 2021Provably Faster Algorithms for Bilevel Optimizationcited by 106
  23. 2022A framework for bilevel optimization that enables stochastic and global variance reduction algorithmscited by 99
  24. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  25. 2017Convergence of Langevin MCMC in KL-divergencecited by 88
  26. 2014A Proximal Stochastic Gradient Method with Progressive Variance Reductioncited by 78
  27. 2021Efficient and Accurate Gradients for Neural SDEscited by 71
  28. 2021A Single-Timescale Method for Stochastic Bilevel Optimizationcited by 69
  29. 2021Amortized Implicit Differentiation for Stochastic Bilevel Optimizationcited by 63
  30. 2021A Novel Convergence Analysis for Algorithms of the Adam Familycited by 50
  31. 2023One-step differentiation of iterative algorithmscited by 28
  32. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  33. 2017Asymptotic Bias of Stochastic Gradient Searchcited by 19
  34. 2023Leveraging the two timescale regime to demonstrate convergence of neural networkscited by 19
  35. 2014Convergence of Stochastic Proximal Gradient Algorithmcited by 17
  36. 2019Normalizing Flows: An Introduction and Review of Current Methodscited by 16
  37. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  38. 2023Unsupervised Discovery of Interpretable Directions in h-space of Pre-trained Diffusion Modelscited by 6

50 most cited of 52 All 52 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 9; 2025: 9; 2026: 6.

24 papers.

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  1. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  2. 2024ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimizationcited by 119
  3. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 61
  4. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 38
  5. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 24
  6. 2024Functional Bilevel Optimization for Machine Learningcited by 20
  7. 2024Attention layers provably solve single-location regressioncited by 17
  8. 2024Bayesian Experimental Design via Contrastive Diffusionscited by 11
  9. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  10. 2024AdjointDEIS: Efficient Gradients for Diffusion Modelscited by 7
  11. 2025Direct Distributional Optimization for Provable Alignment of Diffusion Modelscited by 5
  12. 2025A First-order Generative Bilevel Optimization Framework for Diffusion Modelscited by 4
12 more
  1. 2025DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flowscited by 4
  2. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  3. 2025Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectoriescited by 4
  4. 2025Greed is Good: A Unifying Perspective on Guided Generationcited by 2
  5. 2025Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimizationcited by 1
  6. 2026Efficient Stochastic Optimisation via Sequential Monte Carlocited by 1
  7. 2026Diffusion Fine-tuning with Rewarded Moment Matching Distillationcited by 1
  8. 2024Trading Devil Final: Backdoor attack via Stock market and Bayesian Optimizationcited by 0
  9. 2026Particle-based Generalised Stochastic Optimisationcited by 0
  10. 2026Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Modelscited by 0
  11. 2026Radial Tail Repair: Post-Training Correction for Diffusion and Flow Modelscited by 0
  12. 2026Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Costcited by 0

Similar, not cited

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  1. 2026Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling
  2. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers
  3. 2025Optimal Stepsize for Diffusion Sampling
  4. 2023Fast Diffusion Model
  5. 2023A Geometric Perspective on Diffusion Models
  6. 2024New algorithms for sampling and diffusion models
  7. 2025Fewer Denoising Steps or Cheaper Per-Step Inference: Towards Compute-Optimal Diffusion Model Deployment
  8. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Models