# Lookahead Diffusion Probabilistic Models for Refining Mean Estimation

arXiv: https://arxiv.org/abs/2304.11312 · HTML: https://mlsanity.com/paper/2304.11312/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 22 Apr 2023.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models](https://mlsanity.com/paper/2206.07309/) (2022)
- [BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis](https://mlsanity.com/paper/2203.13508/) (2022)

## Built on by (most cited first, 11 of 11)

- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [Distilling ODE Solvers of Diffusion Models into Smaller Steps](https://mlsanity.com/paper/2309.16421/) (2023)
- [Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions](https://mlsanity.com/paper/2504.01855/) (2025)
- [Frequency Regulation for Exposure Bias Mitigation in Diffusion Models](https://mlsanity.com/paper/2507.10072/) (2025)
- [On Inference Stability for Diffusion Models](https://mlsanity.com/paper/2312.12431/) (2023)
- [Elucidating the SNR-t Bias of Diffusion Probabilistic Models](https://mlsanity.com/paper/2604.16044/) (2026)
- [Bias mitigation in graph diffusion models](https://mlsanity.com/paper/2604.01709/) (2026)
- [BRICS: Bi-level feature Representation of Image CollectionS](https://mlsanity.com/paper/2305.18601/) (2023)
- [SynBoost: A Synergistic Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2506.13058/) (2025)
- [Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplers](https://mlsanity.com/paper/2607.04113/) (2026)
- [D2PO: Optimizing Diffusion Samplers via Dynamic Preference](https://mlsanity.com/paper/2607.06609/) (2026)

## Abstract (arXiv)

We propose lookahead diffusion probabilistic models (LA-DPMs) to exploit the correlation in the outputs of the deep neural networks (DNNs) over subsequent timesteps in diffusion probabilistic models (DPMs) to refine the mean estimation of the conditional Gaussian distributions in the backward process. A typical DPM first obtains an estimate of the original data sample boldsymbolx by feeding the most recent state boldsymbolzi and index i into the DNN model and then computes the mean vector of the conditional Gaussian distribution for boldsymbolzi-1. We propose to calculate a more accurate estimate for boldsymbolx by performing extrapolation on the two estimates of boldsymbolx that are obtained by feeding (boldsymbolzi+1,i+1) and (boldsymbolzi,i) into the DNN model. The extrapolation can be easily integrated into the backward process of existing DPMs by introducing an additional connection over two consecutive timesteps, and fine-tuning is not required. Extensive experiments showed that plugging in the additional connection into DDPM, DDIM, DEIS, S-PNDM, and high-order DPM-Solvers leads to a significant performance gain in terms of FID score.