# Nearest Neighbour Score Estimators for Diffusion Generative Models

arXiv: https://arxiv.org/abs/2402.08018 · HTML: https://mlsanity.com/paper/2402.08018/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Flexible Diffusion Modeling of Long Videos](https://mlsanity.com/paper/2205.11495/) (2022)
- [Nearest Neighbor Machine Translation](https://mlsanity.com/paper/2010.00710/) (2020)
- [KNN-Diffusion: Image Generation via Large-Scale Retrieval](https://mlsanity.com/paper/2204.02849/) (2022)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Stable Target Field for Reduced Variance Score Estimation in Diffusion Models](https://mlsanity.com/paper/2302.00670/) (2023)
- [RetrieveGAN: Image Synthesis via Differentiable Patch Retrieval](https://mlsanity.com/paper/2007.08513/) (2020)
- [On the Generalization of Diffusion Model](https://mlsanity.com/paper/2305.14712/) (2023)
- [RetrievalFuse: Neural 3D Scene Reconstruction with a Database](https://mlsanity.com/paper/2104.00024/) (2021)

## Built on by (most cited first, 10 of 10)

- [Towards a Mechanistic Explanation of Diffusion Model Generalization](https://mlsanity.com/paper/2411.19339/) (2024)
- [Locality in Image Diffusion Models Emerges from Data Statistics](https://mlsanity.com/paper/2509.09672/) (2025)
- [Selective Underfitting in Diffusion Models](https://mlsanity.com/paper/2510.01378/) (2025)
- [Stable Velocity: A Variance Perspective on Flow Matching](https://mlsanity.com/paper/2602.05435/) (2026)
- [Generalization of Diffusion Models Arises with a Balanced Representation Space](https://mlsanity.com/paper/2512.20963/) (2025)
- [Diagnosing and Improving Diffusion Models by Estimating the Optimal Loss Value](https://mlsanity.com/paper/2506.13763/) (2025)
- [Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment](https://mlsanity.com/paper/2510.03335/) (2025)
- [Fast and Scalable Analytical Diffusion](https://mlsanity.com/paper/2602.16498/) (2026)
- [Follow the Mean: Reference-Guided Flow Matching](https://mlsanity.com/paper/2605.10302/) (2026)
- [Filtered Posterior Mean Collections: A Unified Framework for Analytical Models of Diffusion Generalization](https://mlsanity.com/paper/2605.24192/) (2026)

## Abstract (arXiv)

Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo estimators based on the conditional score. We introduce a novel nearest neighbour score function estimator which utilizes multiple samples from the training set to dramatically decrease estimator variance. We leverage our low variance estimator in two compelling applications. Training consistency models with our estimator, we report a significant increase in both convergence speed and sample quality. In diffusion models, we show that our estimator can replace a learned network for probability-flow ODE integration, opening promising new avenues of future research.