# Optimizing Input of Denoising Score Matching is Biased Towards Higher Score Norm

arXiv: https://arxiv.org/abs/2511.11727 · HTML: https://mlsanity.com/paper/2511.11727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Transfer between Modalities with MetaQueries](https://mlsanity.com/paper/2504.06256/) (2025)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Autoregressive Video Generation without Vector Quantization](https://mlsanity.com/paper/2412.14169/) (2024)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Fluid: Scaling Autoregressive Text-to-image Generative Models with Continuous Tokens](https://mlsanity.com/paper/2410.13863/) (2024)
- [HART: Efficient Visual Generation with Hybrid Autoregressive Transformer](https://mlsanity.com/paper/2410.10812/) (2024)
- [Towards image compression with perfect realism at ultra-low bitrates](https://mlsanity.com/paper/2310.10325/) (2023)
- [Autoregressive Speech Synthesis without Vector Quantization](https://mlsanity.com/paper/2407.08551/) (2024)
- [NextStep-1: Toward Autoregressive Image Generation with Continuous Tokens at Scale](https://mlsanity.com/paper/2508.10711/) (2025)
- [Taming Mode Collapse in Score Distillation for Text-to-3D Generation](https://mlsanity.com/paper/2401.00909/) (2023)
- [Flow to the Mode: Mode-Seeking Diffusion Autoencoders for State-of-the-Art Image Tokenization](https://mlsanity.com/paper/2503.11056/) (2025)
- [Frequency Autoregressive Image Generation with Continuous Tokens](https://mlsanity.com/paper/2503.05305/) (2025)
- [DiSA: Diffusion Step Annealing in Autoregressive Image Generation](https://mlsanity.com/paper/2505.20297/) (2025)

## Built on by (most cited first, 1 of 1)

- [CoD: A Diffusion Foundation Model for Image Compression](https://mlsanity.com/paper/2511.18706/) (2025)

## Abstract (arXiv)

Many recent works utilize denoising score matching to optimize the conditional input of diffusion models. In this workshop paper, we demonstrate that such optimization breaks the equivalence between denoising score matching and exact score matching. Furthermore, we show that this bias leads to higher score norm. Additionally, we observe a similar bias when optimizing the data distribution using a pre-trained diffusion model. Finally, we discuss the wide range of works across different domains that are affected by this bias, including MAR for auto-regressive generation, PerCo for image compression, and DreamFusion for text to 3D generation.