# PTQD: Accurate Post-Training Quantization for Diffusion Models

arXiv: https://arxiv.org/abs/2305.10657 · HTML: https://mlsanity.com/paper/2305.10657/

## Key facts

- Cited by 170 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 56 of its 70 references that are in the map.
- First posted on arXiv 18 May 2023.

## Placed in

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

## Builds on (most cited first, 30 of 56)

- [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)
- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)

## Built on by (most cited first, 30 of 170)

- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [DragAnything: Motion Control for Anything using Entity Representation](https://mlsanity.com/paper/2403.07420/) (2024)
- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [FORA: Fast-Forward Caching in Diffusion Transformer Acceleration](https://mlsanity.com/paper/2407.01425/) (2024)
- [FasterCache: Training-Free Video Diffusion Model Acceleration with High Quality](https://mlsanity.com/paper/2410.19355/) (2024)
- [ViDiT-Q: Efficient and Accurate Quantization of Diffusion Transformers for Image and Video Generation](https://mlsanity.com/paper/2406.02540/) (2024)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [Adaptive Caching for Faster Video Generation with Diffusion Transformers](https://mlsanity.com/paper/2411.02397/) (2024)
- [Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2406.17343/) (2024)
- [ZipCache: Accurate and Efficient KV Cache Quantization with Salient Token Identification](https://mlsanity.com/paper/2405.14256/) (2024)
- [Temporal Dynamic Quantization for Diffusion Models](https://mlsanity.com/paper/2306.02316/) (2023)
- [PTQ4DiT: Post-training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2405.16005/) (2024)
- [EfficientDM: Efficient Quantization-Aware Fine-Tuning of Low-Bit Diffusion Models](https://mlsanity.com/paper/2310.03270/) (2023)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [TinyFusion: Diffusion Transformers Learned Shallow](https://mlsanity.com/paper/2412.01199/) (2024)
- [MixDQ: Memory-Efficient Few-Step Text-to-Image Diffusion Models with Metric-Decoupled Mixed Precision Quantization](https://mlsanity.com/paper/2405.17873/) (2024)
- [MagCache: Fast Video Generation with Magnitude-Aware Cache](https://mlsanity.com/paper/2506.09045/) (2025)
- [Paragraph-to-Image Generation with Information-Enriched Diffusion Model](https://mlsanity.com/paper/2311.14284/) (2023)
- [BitsFusion: 1.99 bits Weight Quantization of Diffusion Model](https://mlsanity.com/paper/2406.04333/) (2024)
- [LazyDiT: Lazy Learning for the Acceleration of Diffusion Transformers](https://mlsanity.com/paper/2412.12444/) (2024)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Flow caching for autoregressive video generation](https://mlsanity.com/paper/2602.10825/) (2026)
- [SDXS: Real-Time One-Step Latent Diffusion Models with Image Conditions](https://mlsanity.com/paper/2403.16627/) (2024)
- [EDA-DM: Enhanced Distribution Alignment for Post-Training Quantization of Diffusion Models](https://mlsanity.com/paper/2401.04585/) (2024)
- [DKDM: Data-Free Knowledge Distillation for Diffusion Models with Any Architecture](https://mlsanity.com/paper/2409.03550/) (2024)
- [Importance-Based Token Merging for Efficient Image and Video Generation](https://mlsanity.com/paper/2411.16720/) (2024)

## Abstract (arXiv)

Diffusion models have recently dominated image synthesis tasks. However, the iterative denoising process is expensive in computations at inference time, making diffusion models less practical for low-latency and scalable real-world applications. Post-training quantization (PTQ) of diffusion models can significantly reduce the model size and accelerate the sampling process without re-training. Nonetheless, applying existing PTQ methods directly to low-bit diffusion models can significantly impair the quality of generated samples. Specifically, for each denoising step, quantization noise leads to deviations in the estimated mean and mismatches with the predetermined variance schedule. As the sampling process proceeds, the quantization noise may accumulate, resulting in a low signal-to-noise ratio (SNR) during the later denoising steps. To address these challenges, we propose a unified formulation for the quantization noise and diffusion perturbed noise in the quantized denoising process. Specifically, we first disentangle the quantization noise into its correlated and residual uncorrelated parts regarding its full-precision counterpart. The correlated part can be easily corrected by estimating the correlation coefficient. For the uncorrelated part, we subtract the bias from the quantized results to correct the mean deviation and calibrate the denoising variance schedule to absorb the excess variance resulting from quantization. Moreover, we introduce a mixed-precision scheme for selecting the optimal bitwidth for each denoising step. Extensive experiments demonstrate that our method outperforms previous post-training quantized diffusion models, with only a 0.06 increase in FID score compared to full-precision LDM-4 on ImageNet 256x256, while saving 19.9x bit operations. Code is available at https://github.com/ziplab/PTQD.