# Quantization-Aware Kalman Estimation for Diffusion Sampling

arXiv: https://arxiv.org/abs/2609.21407 · HTML: https://mlsanity.com/paper/2609.21407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [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)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [PixArt-Sigma: Weak-to-Strong Training of Diffusion Transformer for 4K Text-to-Image Generation](https://mlsanity.com/paper/2403.04692/) (2024)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Playground v2.5: Three Insights towards Enhancing Aesthetic Quality in Text-to-Image Generation](https://mlsanity.com/paper/2402.17245/) (2024)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [A Picture is Worth More Than 77 Text Tokens: Evaluating CLIP-Style Models on Dense Captions](https://mlsanity.com/paper/2312.08578/) (2023)
- [Timestep-Aware Correction for Quantized Diffusion Models](https://mlsanity.com/paper/2407.03917/) (2024)
- [Error Propagation Mechanisms and Compensation Strategies for Quantized Diffusion](https://mlsanity.com/paper/2508.12094/) (2025)
- [Test-Time Iterative Error Correction for Efficient Diffusion Models](https://mlsanity.com/paper/2511.06250/) (2025)
- [Q-Drift: Quantization-Aware Drift Correction for Diffusion Model Sampling](https://mlsanity.com/paper/2603.18095/) (2026)
- [D2-DPM: Dual Denoising for Quantized Diffusion Probabilistic Models](https://mlsanity.com/paper/2501.08180/) (2025)

## Abstract (arXiv)

Quantization offers a practical path to deploying diffusion models with reduced memory and computation, but aggressive compression can cause quantized outputs to deviate substantially from their full-precision counterparts. Sampling-stage correction methods seek to compensate for such deviations during sampling, but existing approaches rely primarily on local information and underexploit trajectory history, limiting their ability to correct errors that propagate across timesteps. In this work, we formulate sampling with a quantized denoiser as an online estimation problem, using the history of quantized denoiser outputs to recover the underlying full-precision outputs required by the sampler. We propose QuAKE, a Quantization-Aware Kalman Estimator that combines a smooth trajectory prior with a conditional Gaussian observation model. At each sampling step, QuAKE recursively updates the posterior over the output window in closed form and feeds its posterior mean to the sampler. QuAKE is a lightweight plug-and-play corrector that requires no modification to the quantized network and naturally supports arbitrary high-order multistep ODE samplers. Experiments across W4A4-quantized text-to-image diffusion models show that QuAKE consistently outperforms existing methods in reducing the distributional discrepancy from full-precision sampling.