mlsanityData to 7 Oct 2026

D-Flow: Differentiating through Flows for Controlled Generation

arXiv 2402.14017 ↗First posted 21 Feb 2024cs.LGcited by 115

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all.

Key facts. Cited by 115 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 32 of its 46 references that are in the map. First posted on arXiv 21 Feb 2024.

Builds on

32 of 46 references.

Closest ancestors · 1

Same direction, newest first

  1. 2023Equivariant Flow Matching with Hybrid Probability Transport12 Dec

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2022Classifier-Free Diffusion Guidancecited by 5,717
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  10. 2022Denoising Diffusion Restoration Modelscited by 951
  11. 2022High Fidelity Neural Audio Compressioncited by 673
  12. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
19 more
  1. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  2. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 574
  3. 2023MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generationcited by 529
  4. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  5. 2023Simple and Controllable Music Generationcited by 480
  6. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  7. 2017Compressed Sensing using Generative Modelscited by 337
  8. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  9. 2018Fr'echet Audio Distance: A Metric for Evaluating Music Enhancement Algorithmscited by 221
  10. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  11. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  12. 2023End-to-End Diffusion Latent Optimization Improves Classifier Guidancecited by 107
  13. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  14. 2023Generating images of rare concepts using pre-trained diffusion modelscited by 78
  15. 2024Masked Audio Generation using a Single Non-Autoregressive Transformercited by 50
  16. 2023On Kinetic Optimal Probability Paths for Generative Modelscited by 42
  17. 2020Solving Inverse Problems with a Flow-based Noise Modelcited by 31
  18. 2022Diffeomorphic Counterfactuals with Generative Modelscited by 29
  19. 2021Generative Flows as a General Purpose Solution for Inverse Problemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 20; 2025: 47; 2026: 48.

115 papers.

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  1. 2025Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Stepscited by 225
  2. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  3. 2024ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimizationcited by 115
  4. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  5. 2024Not All Noises Are Created Equally:Diffusion Noise Selection and Optimizationcited by 70
  6. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 59
  7. 2024Diffusion Models and Representation Learning: A Surveycited by 53
  8. 2024Inference-Time Alignment of Diffusion Models with Direct Noise Optimizationcited by 51
  9. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  10. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  11. 2025On the Guidance of Flow Matchingcited by 44
  12. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 40
38 more
  1. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  2. 2025Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcingcited by 37
  3. 2024Gradient-Free Generation for Hard-Constrained Systemscited by 35
  4. 2025Noise Hypernetworks: Amortizing Test-Time Compute in Diffusion Modelscited by 35
  5. 2026Meta Flow Maps enable scalable reward alignmentcited by 32
  6. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  7. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 26
  8. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 25
  9. 2024Training Free Guided Flow Matching with Optimal Controlcited by 23
  10. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 23
  11. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  12. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regionscited by 19
  13. 2024Fast and Robust Visuomotor Riemannian Flow Matching Policycited by 18
  14. 2025GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Modelscited by 17
  15. 2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 17
  16. 2025HOIDiNi: Human-Object Interaction through Diffusion Noise Optimizationcited by 16
  17. 2024Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costscited by 14
  18. 2024RectifID: Personalizing Rectified Flow with Anchored Classifier Guidancecited by 11
  19. 2025LanPaint: Training-Free Diffusion Inpainting with Asymptotically Exact and Fast Conditional Samplingcited by 11
  20. 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
  21. 2025Source-Guided Flow Matchingcited by 11
  22. 2025ORIGEN: Zero-Shot 3D Orientation Grounding in Text-to-Image Generationcited by 10
  23. 2025It's Never Too Late: Noise Optimization for Collapse Recovery in Trained Diffusion Modelscited by 9
  24. 2025Adjusting Initial Noise to Mitigate Memorization in Text-to-Image Diffusion Modelscited by 7
  25. 2024Adaptive Diffusion Terrain Generator for Autonomous Uneven Terrain Navigationcited by 6
  26. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  27. 2024Posterior sampling via Langevin dynamics based on generative priorscited by 5
  28. 2025MAP Estimation with Denoisers: Convergence Rates and Guaranteescited by 5
  29. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  30. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  31. 2026How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidancecited by 5
  32. 2025TFG-Flow: Training-free Guidance in Multimodal Generative Flowcited by 4
  33. 2025A Variational Perspective on Generative Protein Fitness Optimizationcited by 4
  34. 2025Energy-Based Flow Matching for Generating 3D Molecular Structurecited by 4
  35. 2025SONIC: Spectral Optimization of Noise for Inpainting with Consistencycited by 4
  36. 2026Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performancecited by 4
  37. 2026Safety-Guided Flow (SGF): A Unified Framework for Negative Guidance in Safe Generationcited by 4
  38. 2025FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problemscited by 3

50 most cited of 115 All 115 (JSON)

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  1. 2025An Introduction to Flow Matching and Diffusion Models
  2. 2024Exploring Diffusion and Flow Matching Under Generator Matching
  3. 2025LeDiFlow: Learned Distribution-guided Flow Matching to Accelerate Image Generation
  4. 2024Local Flow Matching Generative Models
  5. 2026Drift Flow Matching
  6. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning
  7. 2025The Generation Phases of Flow Matching: a Denoising Perspective
  8. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generation