mlsanityData to 7 Oct 2026

Variance-Reduced Diffusion Sampling via Target Score Identity

arXiv 2601.01594 ↗First posted 4 Jan 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal score as a conditional expectation of the target score under the forward diffusion, we develop: (i) a plug-and-play nonparametric self-normalized importance sampling estimator compatible with standard reverse-time solvers, (ii) a variance-minimizing state- and time-dependent blending rule between Tweedie-type and TSI estimators together with an anti-correlation analysis, (iii) a data-only extension based on locally fitted proxy scores, and (iv) a likelihood-tilting extension to Bayesian inverse problems. We also propose a Critic--Gate distillation scheme that amortizes the state-dependent blending coefficient into a neural gate. Experiments on synthetic targets and PDE-governed inverse problems demonstrate improved sample quality for a fixed simulation budget.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 29 of its 70 references that are in the map. First posted on arXiv 4 Jan 2026.

Builds on

29 of 70 references.

Closest ancestors · 12

Same direction, newest first

  1. 2025Control Variate Score Matching for Diffusion Models23 Dec
  2. 2024Target Score Matching13 Feb
  3. 2024Particle Denoising Diffusion Sampler9 Feb
  4. 2023Consistency Models2 Mar
  5. 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation9 Oct
  6. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  8. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  9. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 17

  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2016A Kernel Test of Goodness of Fitcited by 143
  4. 2019Mean estimation and regression under heavy-tailed distributions--a surveycited by 133
  5. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  6. 2019Maximum Mean Discrepancy Gradient Flowcited by 123
  7. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  8. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  9. 2021Kernel Stein Discrepancy Descentcited by 57
  10. 2013Density Estimation in Infinite Dimensional Exponential Familiescited by 41
  11. 2018Learning deep kernels for exponential family densitiescited by 36
  12. 2013A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversioncited by 32
5 more
  1. 2020Nonparametric Score Estimatorscited by 22
  2. 2024Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equationscited by 22
  3. 2022Posterior samples of source galaxies in strong gravitational lenses with score-based priorscited by 20
  4. 2017Kernel Conditional Exponential Familycited by 7
  5. 2025Simulating Fokker-Planck equations via mean field control of score-based normalizing flowscited by 3

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  1. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Models
  2. 2026Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
  3. 2023Denoising Diffusion Samplers
  4. 2025Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
  5. 2025Faster Diffusion Models via Higher-Order Approximation
  6. 2025Importance Weighted Score Matching for Diffusion Samplers with Enhanced Mode Coverage
  7. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  8. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models