mlsanityData to 7 Oct 2026

Target Score Matching

arXiv 2402.08667 ↗First posted 13 Feb 2024cs.LG stat.CO stat.MLcited by 46

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 24 of its 33 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

24 of 33 references.

Closest ancestors · 12

Same direction, newest first

  1. 2023Non-Denoising Forward-Time Diffusions22 Dec
  2. 2023Generative Diffusion Models for Lattice Field Theory6 Nov
  3. 2023Scaling Riemannian Diffusion Models30 Oct
  4. 2023Renormalizing Diffusion Models23 Aug
  5. 2023Denoising Diffusion Samplers27 Feb
  6. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  7. 2022Riemannian Diffusion Models16 Aug
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  9. 2022Riemannian Score-Based Generative Modelling6 Feb
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 12

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  4. 2023SE(3) diffusion model with application to protein backbone generationcited by 214
  5. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  6. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  7. 2023Improved sampling via learned diffusionscited by 103
  8. 2023Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamicscited by 72
  9. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  10. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  11. 2023Reverse Diffusion Monte Carlocited by 41
  12. 2020A Wasserstein Minimum Velocity Approach to Learning Unnormalized Modelscited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 24; 2026: 12.

46 papers.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  3. 2024Schr"odinger Bridge Flow for Unpaired Data Translationcited by 47
  4. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  5. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  6. 2025Accelerated Diffusion Models via Speculative Samplingcited by 30
  7. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 28
  8. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  9. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  10. 2025Target Concrete Score Matching: A Holistic Framework for Discrete Diffusioncited by 25
  11. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  12. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
34 more
  1. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  2. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 16
  3. 2025Proximal Diffusion Neural Samplercited by 16
  4. 2025FEAT: Free energy Estimators with Adaptive Transportcited by 15
  5. 2024Variational Distillation of Diffusion Policies into Mixture of Expertscited by 14
  6. 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
  7. 2025Progressive Tempering Sampler with Diffusioncited by 13
  8. 2025Amortized Sampling with Transferable Normalizing Flowscited by 11
  9. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  10. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  11. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 8
  12. 2024Solvation Free Energies from Neural Thermodynamic Integrationcited by 7
  13. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
  14. 2024Hamiltonian Score Matching and Generative Flowscited by 6
  15. 2024Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusioncited by 4
  16. 2025In-Context Parametric Inference: Point or Distribution Estimators?cited by 4
  17. 2025Control Variate Score Matching for Diffusion Modelscited by 4
  18. 2026Discrete Adjoint Schr"odinger Bridge Samplercited by 4
  19. 2026Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processescited by 4
  20. 2025Energy-based generator matching: A neural sampler for general state spacecited by 3
  21. 2025Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlocited by 3
  22. 2025Fine-Tuning Diffusion Models via Intermediate Distribution Shapingcited by 3
  23. 2025Exploring Structured Semantic Priors Underlying Diffusion Score for Test-time Adaptationcited by 2
  24. 2025Sampling from Energy distributions with Target Concrete Score Identitycited by 2
  25. 2026Diffusion Path Samplers via Sequential Monte Carlocited by 2
  26. 2026Inverting Data Transformations via Diffusion Samplingcited by 2
  27. 2025Dimension-free Score Matching and Time Bootstrapping for Diffusion Modelscited by 1
  28. 2026Latent Target Score Matching, with an application to Simulation-Based Inferencecited by 1
  29. 2026ATLAS: A Foundation Neural Sampler for Amorphous Materialscited by 1
  30. 2026Variance-Reduced Diffusion Sampling via Target Score Identitycited by 0
  31. 2026A Priori Sampling of Transition States with Guided Diffusioncited by 0
  32. 2026An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generationcited by 0
  33. 2026FES-FM: Free Energy Surface Sampling via Reduced Flow Matchingcited by 0
  34. 2026DriftOPD: Sequence-Level Reverse-KL Distillation for One-Step VLA Policiescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers
  2. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridges
  3. 2025Optimizing Input of Denoising Score Matching is Biased Towards Higher Score Norm
  4. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Models
  5. 2024From optimal score matching to optimal sampling
  6. 2022From Denoising Diffusions to Denoising Markov Models
  7. 2025Heteroscedasticity of Denoising Score Matching with Generalised Smooth Noise
  8. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves