# Deflating the Hessian: Rank-4 W4A4 Quantization for Multimodal Diffusion Transformers

arXiv: https://arxiv.org/abs/2610.11315 · HTML: https://mlsanity.com/paper/2610.11315/

## 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 9 of its 31 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [Playground v2.5: Three Insights towards Enhancing Aesthetic Quality in Text-to-Image Generation](https://mlsanity.com/paper/2402.17245/) (2024)
- [OrbitQuant: Data-Agnostic Quantization for Image and Video Diffusion Transformers](https://mlsanity.com/paper/2607.02461/) (2026)
- [DiRotQ: Rotation-Aware Quantization for 4-bit Diffusion Transformers](https://mlsanity.com/paper/2605.16732/) (2026)
- [Low-Rank Correction for Quantized LLMs](https://mlsanity.com/paper/2412.07902/) (2024)
- [LoRaQ: Optimized Low Rank Approximation for 4-bit Quantization](https://mlsanity.com/paper/2604.18117/) (2026)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)

## Abstract (arXiv)

In diffusion transformers, low-rank branches can mitigate 4-bit weight--activation (W4A4) post-training quantization (PTQ) loss by decomposing each weight into a low-bit residual and a high-precision low-rank component. Existing low-rank PTQ approaches, however, either optimize low-rank compensation and residual quantization separately, often requiring higher ranks, or rely on second-order weight updates without explicitly modeling activation quantization error, which becomes particularly pronounced under 4-bit quantization. To address these limitations, we present HSVDQuant, a unified framework modeling low-rank-assisted W4A4 PTQ as a coupled calibration problem and deriving optimization-based solvers from the joint objective. Eliminating the output-side low-rank factor yields a deflated Hessian that discounts residual errors already captured by the low-rank component, while an activation-noise surrogate is incorporated to suppress activation quantization error. Across five diffusion backbones, rank-4 HSVDQuant consistently outperforms rank-4 SVDQuant in PSNR and LPIPS. It further surpasses rank-32 SVDQuant on SANA-1.6B, FLUX.1-schnell, and FLUX.1-dev with an 8× smaller rank and up to 6.25× faster quantization. Furthermore, on the Qwen3-8B LLM, rank-4 HSVDQuant improves MMLU accuracy from 61.50% to 68.17% over rank-32 SVDQuant. Overall, HSVDQuant achieves better W4A4 performance with substantially lower rank and quantization cost.