mlsanityData to 14 Oct 2026

Spatially Adaptive Noise Injection

arXiv 2609.18466 ↗First posted 16 Sep 2026cs.LG stat.MLcited by 1

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Diffusion samplers reverse a learned noising process using either stochastic (DDPM) or deterministic (DDIM) updates, which represent endpoints of a single family controlled by a scalar noise-injection variance that is applied identically at every spatial location. This uniform approach neglects the geometry of natural images: high-curvature regions such as edges and textures, where the denoiser is uncertain, benefit from stochastic correction, whereas smooth regions, where the score is precise, are degraded by injected noise. This work investigates whether each pixel requires stochastic correction at a given timestep and introduces Spatially Adaptive Noise Injection (SANI), a novel sampling framework that dynamically adjusts noise application on a per-pixel basis. SANI integrates a probabilistic gating mechanism with a derived spatially adaptive variance, ensuring that noise is injected precisely where needed to refine complex features while preserving well-formed structures. Experimental results and decoupling ablations demonstrate that SANI consistently improves Fr'echet Inception Distance (FID) over the vanilla DDPM and DDIM endpoint samplers across diverse sampling timesteps, while remaining competitive with variance-learning baselines, highlighting the importance of spatial adaptivity in diffusion sampling.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 22 of its 25 references that are in the map. First posted on arXiv 16 Sep 2026.

Builds on

22 of 25 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep

Other references · 21

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Denoising Diffusion Implicit Modelscited by 9,781
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2022Scalable Diffusion Models with Transformerscited by 6,054
  5. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  7. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
  8. 2021Variational Diffusion Modelscited by 1,153
  9. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 938
  10. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 334
  11. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Modelscited by 83
  12. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 64
9 more
  1. 2023Diffusion Models With Learned Adaptive Noisecited by 51
  2. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantificationcited by 33
  3. 2025Region-Adaptive Sampling for Diffusion Transformerscited by 33
  4. 2025Generative Uncertainty in Diffusion Modelscited by 23
  5. 2024Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimationcited by 20
  6. 2024Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matchingcited by 13
  7. 2021A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applicationscited by 9
  8. 2026Denoising, Fast and Slow: Difficulty-Aware Adaptive Sampling for Image Generationcited by 5
  9. 2024High Frequency Matters: Uncertainty Guided Image Compression with Wavelet Diffusioncited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026ExploreNet: Learning Where to Explore in Diffusion GRPOcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026ASSERT: Adaptive Stochastic Sampling for Robust Diffusion Models on Analog Compute-in-Memory Hardware
  2. 2023SVNR: Spatially-variant Noise Removal with Denoising Diffusion
  3. 2024Diffusion Priors for Variational Likelihood Estimation and Image Denoising
  4. 2025BUFF: Bayesian Uncertainty Guided Diffusion Probabilistic Model for Single Image Super-Resolution
  5. 2026AsyncPatch Diffusion: spatially-flexible image generation
  6. 2024Enhancing Sample Generation of Diffusion Models using Noise Level Correction
  7. 2026Stochastic Optimal Control Sampling for Diffusion Inverse Problems
  8. 2025Accelerating Diffusion-based Super-Resolution with Dynamic Time-Spatial Sampling