# Diffusion Product Quantization

arXiv: https://arxiv.org/abs/2411.12306 · HTML: https://mlsanity.com/paper/2411.12306/

## 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 22 of its 39 references that are in the map.
- First posted on arXiv 19 Nov 2024.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2406.17343/) (2024)
- [GPTVQ: The Blessing of Dimensionality for LLM Quantization](https://mlsanity.com/paper/2402.15319/) (2024)
- [And the Bit Goes Down: Revisiting the Quantization of Neural Networks](https://mlsanity.com/paper/1907.05686/) (2019)
- [VQ4DiT: Efficient Post-Training Vector Quantization for Diffusion Transformers](https://mlsanity.com/paper/2408.17131/) (2024)

## Abstract (arXiv)

In this work, we explore the quantization of diffusion models in extreme compression regimes to reduce model size while maintaining performance. We begin by investigating classical vector quantization but find that diffusion models are particularly susceptible to quantization error, with the codebook size limiting generation quality. To address this, we introduce product quantization, which offers improved reconstruction precision and larger capacity -- crucial for preserving the generative capabilities of diffusion models. Furthermore, we propose a method to compress the codebook by evaluating the importance of each vector and removing redundancy, ensuring the model size remaining within the desired range. We also introduce an end-to-end calibration approach that adjusts assignments during the forward pass and optimizes the codebook using the DDPM loss. By compressing the model to as low as 1 bit (resulting in over 24 times reduction in model size), we achieve a balance between compression and quality. We apply our compression method to the DiT model on ImageNet and consistently outperform other quantization approaches, demonstrating competitive generative performance.