# Softmax Bias Correction for Quantized Generative Models

arXiv: https://arxiv.org/abs/2309.01729 · HTML: https://mlsanity.com/paper/2309.01729/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [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)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [SnapFusion: Text-to-Image Diffusion Model on Mobile Devices within Two Seconds](https://mlsanity.com/paper/2306.00980/) (2023)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers](https://mlsanity.com/paper/2211.16056/) (2022)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [Speed Is All You Need: On-Device Acceleration of Large Diffusion Models via GPU-Aware Optimizations](https://mlsanity.com/paper/2304.11267/) (2023)
- [Neural Network Quantization with AI Model Efficiency Toolkit (AIMET)](https://mlsanity.com/paper/2201.08442/) (2022)

## Built on by (most cited first, 15 of 15)

- [Clockwork Diffusion: Efficient Generation With Model-Step Distillation](https://mlsanity.com/paper/2312.08128/) (2023)
- [Mobile Video Diffusion](https://mlsanity.com/paper/2412.07583/) (2024)
- [Efficient Quantization Strategies for Latent Diffusion Models](https://mlsanity.com/paper/2312.05431/) (2023)
- [Not All Prompts Are Made Equal: Prompt-based Pruning of Text-to-Image Diffusion Models](https://mlsanity.com/paper/2406.12042/) (2024)
- [RefQSR: Reference-based Quantization for Image Super-Resolution Networks](https://mlsanity.com/paper/2404.01690/) (2024)
- [Diffusion Model Quantization: A Review](https://mlsanity.com/paper/2505.05215/) (2025)
- [Temporal Feature Matters: A Framework for Diffusion Model Quantization](https://mlsanity.com/paper/2407.19547/) (2024)
- [SoftmAP: Software-Hardware Co-design for Integer-Only Softmax on Associative Processors](https://mlsanity.com/paper/2411.17847/) (2024)
- [Q-Drift: Quantization-Aware Drift Correction for Diffusion Model Sampling](https://mlsanity.com/paper/2603.18095/) (2026)
- [DPQ-HD: Post-Training Compression for Ultra-Low Power Hyperdimensional Computing](https://mlsanity.com/paper/2505.05413/) (2025)
- [Text Embedding Knows How to Quantize Text-Guided Diffusion Models](https://mlsanity.com/paper/2507.10340/) (2025)
- [A KL Lens on Quantization: Fast, Forward-Only Sensitivity for Mixed-Precision SSM-Transformer Models](https://mlsanity.com/paper/2604.13440/) (2026)
- [Quantized Keys Steal Attention: Bias Correction for KV-Cache Compression in Video Diffusion](https://mlsanity.com/paper/2605.26266/) (2026)
- [QMC: Efficient SLM Edge Inference via Outlier-Aware Quantization and Emergent Memories Co-Design](https://mlsanity.com/paper/2601.14549/) (2026)
- [Integrated electro-optic attention nonlinearities for transformers](https://mlsanity.com/paper/2604.09512/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) is the go-to compression technique for large generative models, such as stable diffusion or large language models. PTQ methods commonly keep the softmax activation in higher precision as it has been shown to be very sensitive to quantization noise. However, this can lead to a significant runtime and power overhead during inference on resource-constraint edge devices. In this work, we investigate the source of the softmax sensitivity to quantization and show that the quantization operation leads to a large bias in the softmax output, causing accuracy degradation. To overcome this issue, we propose an offline bias correction technique that improves the quantizability of softmax without additional compute during deployment, as it can be readily absorbed into the quantization parameters. We demonstrate the effectiveness of our method on stable diffusion v1.5 and 125M-size OPT language model, achieving significant accuracy improvement for 8-bit quantized softmax.