# Diffusion foundations and sampling

Area: [Diffusion models](https://mlsanity.com/diffusion/index.md). HTML: https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/

## Key facts

- Diffusion foundations and sampling: 2,909 papers on arXiv since 2020 (data through 7 Oct 2026).
- 2,359 of its 2,909 mapped papers (81%) cite “Denoising Diffusion Probabilistic Models” (2020, arXiv 2006.11239).
- 1,781 of its 2,909 mapped papers (61%) cite “Score-Based Generative Modeling through Stochastic Differential Equations” (2020, arXiv 2011.13456).
- 83 new papers 17 Sep–7 Oct.

## Most cited here

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020), cited by 2,359 papers here
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020), cited by 1,781 papers here
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021), cited by 1,697 papers here
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020), cited by 1,438 papers here
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021), cited by 1,409 papers here
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022), cited by 884 papers here
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022), cited by 812 papers here
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022), cited by 783 papers here
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021), cited by 772 papers here
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022), cited by 679 papers here

## New (17 Sep–7 Oct)

- [Enabling Preference-driven Unlearning in Few-step Distilled Text-to-Image Diffusion Models](https://mlsanity.com/paper/2610.10859/) (2026-10-07)
- [How Many Directions Must a Truncated Diffusion Sampler Retain? Matching Bounds Under Power-Law Spectra](https://mlsanity.com/paper/2610.10640/) (2026-10-07)
- [Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements](https://mlsanity.com/paper/2610.10366/) (2026-10-07)
- [Universal Local Error and Realized Amplification for the First-Order EDM Predictor](https://mlsanity.com/paper/2610.10190/) (2026-10-07)
- [Think Before You Paint: Recursive Latent Reasoning for Diffusion Models](https://mlsanity.com/paper/2610.09876/) (2026-10-07)
- [Consistent Distribution Matching for Data-Free Diffusion Distillation](https://mlsanity.com/paper/2610.09221/) (2026-10-06)
- [Lower Bounds for Parallel Diffusion Sampling](https://mlsanity.com/paper/2610.09166/) (2026-10-06)
- [Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models](https://mlsanity.com/paper/2610.09045/) (2026-10-06)
- [Feature Information Dynamics in Diffusion](https://mlsanity.com/paper/2610.08626/) (2026-10-06)
- [Two Halves are More than One: Phase-wise Velocity Distillation for Fast and High-Quality Image Generation](https://mlsanity.com/paper/2610.08070/) (2026-10-06)
- [Uniform Discrete Diffusion Models are Minimax Optimal for Estimating Distributions with Small Effective Support Size](https://mlsanity.com/paper/2610.07655/) (2026-10-06)
- [CentriQ: Calibration-Free Quantization of Diffusion Transformers via Exact Mean Centering](https://mlsanity.com/paper/2610.06260/) (2026-10-05)
- [CACFG: Curvature-Aware Classifier-Free Guidance and Optimal Control](https://mlsanity.com/paper/2610.05845/) (2026-10-05)
- [Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data](https://mlsanity.com/paper/2610.05825/) (2026-10-05)
- [Should We Skip Diffusion?](https://mlsanity.com/paper/2610.07002/) (2026-10-04)
- [Cross-Time Directional Selection in Diffusion Sampling](https://mlsanity.com/paper/2610.05199/) (2026-10-04)
- [Best-of-N Guidance for Test-time Diffusion Alignment](https://mlsanity.com/paper/2610.05108/) (2026-10-04)
- [D-DOIT: Training-free Adaptation of Discrete Diffusion via Doob's h-Transform](https://mlsanity.com/paper/2610.04938/) (2026-10-04)
- [Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking](https://mlsanity.com/paper/2610.04568/) (2026-10-03)
- [Discrete Diffusion for Large Graph Generation via Structural Candidate Restriction](https://mlsanity.com/paper/2610.04056/) (2026-10-02)
- [Probability flow ODEs in score-based and reflected diffusion models](https://mlsanity.com/paper/2610.03846/) (2026-10-02)
- [IDRF: Inverse-Distilled Reward Fine-tuning of Masked Discrete Diffusion Models](https://mlsanity.com/paper/2610.03641/) (2026-10-02)
- [Rethinking What to Cache in Few-Step Diffusion Transformers: Solver-Aware Target Selection](https://mlsanity.com/paper/2610.03577/) (2026-10-02)
- [Iterating Consistency Models: Stability, Error Bounds and Noise Schedules](https://mlsanity.com/paper/2610.03414/) (2026-10-02)
- [Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling](https://mlsanity.com/paper/2610.03034/) (2026-10-02)
- [Controlling Polar Exposure to Delay Memorization in Diffusion Models](https://mlsanity.com/paper/2610.02780/) (2026-10-02)
- [Jumping up and down: Denoiser diffusion models for discrete ordinal data](https://mlsanity.com/paper/2610.02754/) (2026-10-02)
- [Correcting Guided Diffusion Trajectories with Spectral Alignment](https://mlsanity.com/paper/2610.02753/) (2026-10-02)
- [Embedding Prediction Helps Image Generation](https://mlsanity.com/paper/2610.02203/) (2026-10-01)
- [Sample complexity bounds for categorical Markov random fields via Discrete Diffusions](https://mlsanity.com/paper/2610.02128/) (2026-10-01)