mlsanityData to 14 Oct 2026

RNE: plug-and-play diffusion inference-time control and energy-based training

arXiv 2506.05668 ↗First posted 6 Jun 2025cs.LG stat.MLcited by 17

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the textitdensity ratio between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies (1) diffusion density estimation, (2) inference-time control, and (3) energy-based diffusion training under a single perspective. Experiments demonstrate that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance, and achieves a simple yet efficient regularisation for training energy-based diffusion models. Additionally, our proposed RNE is modality-agnostic and applicable not only to continuous diffusion models but also to their discrete diffusion counterparts.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 68 of its 94 references that are in the map. First posted on arXiv 6 Jun 2025.

Builds on

68 of 94 references.

Closest ancestors · 28

Same direction, newest first

  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts4 Mar
  2. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo18 Feb
  3. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo10 Feb
  4. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review16 Jan
  5. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan
  6. 2024The Superposition of Diffusion Models Using the Ito Density Estimator23 Dec
  7. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regions2 Nov
  8. 2024Learned Reference-based Diffusion Sampling for multi-modal distributions25 Oct
  9. 2024Diffusion Density Estimators9 Oct
  10. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform3 Jun
  11. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints28 Feb
  12. 2024Target Score Matching13 Feb
16 more
  1. 2024Particle Denoising Diffusion Sampler9 Feb
  2. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers16 Jan
  3. 2023Denoising Diffusion Samplers27 Feb
  4. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC22 Feb
  5. 2022Classifier-Free Diffusion Guidance26 Jul
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  7. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  8. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  9. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  10. 2021Variational Diffusion Models1 Jul
  11. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  12. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  13. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  14. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  15. 2020Denoising Diffusion Implicit Models6 Oct
  16. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 40

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2022Video Diffusion Modelscited by 2,305
  4. 2016Variational Inference: A Review for Statisticianscited by 1,472
  5. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  6. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  7. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  8. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
  9. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  10. 2022Compositional Visual Generation with Composable Diffusion Modelscited by 624
  11. 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Datacited by 381
  12. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
28 more
  1. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
  2. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 233
  3. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  4. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 217
  5. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 177
  6. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  7. 2023Compositional Foundation Models for Hierarchical Planningcited by 95
  8. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  9. 2023Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamicscited by 72
  10. 2024NETS: A Non-Equilibrium Transport Samplercited by 69
  11. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
  12. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  13. 2024Sequential Controlled Langevin Diffusionscited by 48
  14. 2023OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentialscited by 47
  15. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 38
  16. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 31
  17. 2023Accurate transition state generation with an object-aware equivariant elementary reaction diffusion modelcited by 30
  18. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 28
  19. 2024Diffusion Soup: Model Merging for Text-to-Image Diffusion Modelscited by 26
  20. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 19
  21. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  22. 2025Learning normalized image densities via dual score matchingcited by 18
  23. 2025Accelerated Parallel Tempering via Neural Transportscited by 17
  24. 2025FEAT: Free energy Estimators with Adaptive Transportcited by 16
  25. 2024Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Modelscited by 14
  26. 2022Towards Healing the Blindness of Score Matchingcited by 13
  27. 2024Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Designcited by 11
  28. 2024Solvation Free Energies from Neural Thermodynamic Integrationcited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 14.

17 papers.

Sort:

By area:

  1. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 23
  2. 2026Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamicscited by 7
  3. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 6
  4. 2025Assessing generative modeling approaches for free energy estimates in condensed mattercited by 3
  5. 2026Compression as Adaptation: Implicit Visual Representation with Diffusion Foundation Modelscited by 2
  6. 2026Towards accurate extreme event likelihoods from diffusion model climate emulatorscited by 2
  7. 2026Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measurescited by 2
  8. 2026Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differencescited by 2
  9. 2026ATLAS: A Foundation Neural Sampler for Amorphous Materialscited by 1
  10. 2026Recipes for Steering and Scaling LLMs via Samplingcited by 1
  11. 2026METALICA: METAdynamics and repLICA exchange for enhanced diffusion samplingcited by 1
  12. 2026Tilted Schr"odinger Bridge Matchingcited by 1
5 more
  1. 2026From Global to Factor-Wise Expert Composition in Discrete Diffusion Modelscited by 0
  2. 2026A Mean-Field Framework for Inference-Time Distributional Control of Diffusion Modelscited by 0
  3. 2026Specificity-Aware Diffusion Steering via Variance-Reduced Sequential Monte Carlocited by 0
  4. 2026Error-Corrected Inference-Time Scaling for Imperfect Diffusion Modelscited by 0
  5. 2026ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Diffusion Models: A Mathematical Introduction
  2. 2025DiffPro: Joint Timestep and Layer-Wise Precision Optimization for Efficient Diffusion Inference
  3. 2024Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference
  4. 2026Fast and Scalable Analytical Diffusion
  5. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  6. 2026Diversify Diffusion with Temperature Sampling and Variance-Corrective Time Shifting
  7. 2026Uniform Diffusion Models Revisited: Leave-One-Out Denoiser and Absorbing State Reformulation
  8. 2025Pretrained Diffusion Models Are Inherently Skipped-Step Samplers