mlsanityData to 7 Oct 2026

Score-Optimal Diffusion Schedules

arXiv 2412.07877 ↗First posted 10 Dec 2024stat.ML cs.LGcited by 16

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data distribution by incrementally injecting noise into the data. To numerically simulate the sampling process, a discretisation schedule from the reference back towards clean data must be chosen. An appropriate discretisation schedule is crucial to obtain high quality samples. However, beyond hand crafted heuristics, a general method for choosing this schedule remains elusive. This paper presents a novel algorithm for adaptively selecting an optimal discretisation schedule with respect to a cost that we derive. Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training. We find that our learned schedule recovers performant schedules previously only discovered through manual search and obtains competitive FID scores on image datasets.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 15 of its 24 references that are in the map. First posted on arXiv 10 Dec 2024.

Builds on

15 of 24 references.

Closest ancestors · 11

Same direction, newest first

  1. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Models22 Apr
  2. 2024Accelerating Diffusion Sampling with Optimized Time Steps27 Feb
  3. 2023Image generation with shortest path diffusion1 Jun
  4. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces18 May
  5. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  7. 2021Variational Diffusion Models1 Jul
  8. 2021Learning to Efficiently Sample from Diffusion Probabilistic Models7 Jun
  9. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 4

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  4. 2021Annealed Flow Transport Monte Carlocited by 90

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 8; 2026: 8.

16 papers.

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  1. 2025A Fourier Space Perspective on Diffusion Modelscited by 48
  2. 2025Spectral Analysis of Diffusion Models with Application to Schedule Designcited by 12
  3. 2025The Cosine Schedule is Fisher-Rao-Optimal for Masked Discrete Diffusion Modelscited by 11
  4. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
  5. 2025Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Modelscited by 6
  6. 2025Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysiscited by 6
  7. 2026Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timestepscited by 3
  8. 2025GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generationcited by 1
  9. 2025Weighted Conditional Flow Matchingcited by 1
  10. 2026Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Modelscited by 1
  11. 2026StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoisercited by 1
  12. 2026Metropolis-Adjusted Diffusion Modelscited by 1
4 more
  1. 2026From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regimecited by 1
  2. 2026A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Modelscited by 0
  3. 2026Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matchingcited by 0
  4. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridgescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Denoising Diffusion Samplers
  2. 2026Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories
  3. 2023Fast Inference in Denoising Diffusion Models via MMD Finetuning
  4. 2024Constant Rate Scheduling: A General Framework for Optimizing Diffusion Noise Schedule via Distributional Change
  5. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  6. 2024Learning to Discretize Denoising Diffusion ODEs
  7. 2026Blind denoising diffusion models and the blessings of dimensionality
  8. 2025Optimal Convergence Analysis of DDPM for General Distributions