# Equipping Diffusion Models with Differentiable Spatial Entropy for Low-Light Image Enhancement

arXiv: https://arxiv.org/abs/2404.09735 · HTML: https://mlsanity.com/paper/2404.09735/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 36 of its 67 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 36)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Deep Retinex Decomposition for Low-Light Enhancement](https://mlsanity.com/paper/1808.04560/) (2018)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Zero-Reference Deep Curve Estimation for Low-Light Image Enhancement](https://mlsanity.com/paper/2001.06826/) (2020)
- [EnlightenGAN: Deep Light Enhancement without Paired Supervision](https://mlsanity.com/paper/1906.06972/) (2019)
- [Kindling the Darkness: A Practical Low-light Image Enhancer](https://mlsanity.com/paper/1905.04161/) (2019)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Learning Enriched Features for Real Image Restoration and Enhancement](https://mlsanity.com/paper/2003.06792/) (2020)
- [Retinex-inspired Unrolling with Cooperative Prior Architecture Search for Low-light Image Enhancement](https://mlsanity.com/paper/2012.05609/) (2020)
- [Retinexformer: One-stage Retinex-based Transformer for Low-light Image Enhancement](https://mlsanity.com/paper/2303.06705/) (2023)
- [Restoring Vision in Adverse Weather Conditions with Patch-Based Denoising Diffusion Models](https://mlsanity.com/paper/2207.14626/) (2022)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Generative Diffusion Prior for Unified Image Restoration and Enhancement](https://mlsanity.com/paper/2304.01247/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Low-Light Image Enhancement with Wavelet-based Diffusion Models](https://mlsanity.com/paper/2306.00306/) (2023)
- [Embedding Fourier for Ultra-High-Definition Low-Light Image Enhancement](https://mlsanity.com/paper/2302.11831/) (2023)

## Built on by (most cited first, 3 of 3)

- [Taming Diffusion Models for Image Restoration: A Review](https://mlsanity.com/paper/2409.10353/) (2024)
- [Diffusion Models for Low-Light Image Enhancement: A Multi-Perspective Taxonomy and Performance Analysis](https://mlsanity.com/paper/2510.05976/) (2025)
- [TAPAS: Throughput-adaptive Perception for Autonomous Systems](https://mlsanity.com/paper/2607.17317/) (2026)

## Abstract (arXiv)

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based works simply employ l1 loss to train their network in a deterministic way, resulting in over-smoothed predictions with inferior perceptual quality. In this work, we propose a novel method that shifts the focus from a deterministic pixel-by-pixel comparison to a statistical perspective, emphasizing the learning of distributions rather than individual pixel values. The core idea is to introduce spatial entropy into the loss function to measure the distribution difference between predictions and targets. To make this spatial entropy differentiable, we employ kernel density estimation (KDE) to approximate the probabilities for specific intensity values of each pixel with their neighbor areas. Specifically, we equip the entropy with diffusion models and aim for superior accuracy and enhanced perceptual quality over l1 based noise matching loss. In the experiments, we evaluate the proposed method for low light enhancement on two datasets and the NTIRE challenge 2024. All these results illustrate the effectiveness of our statistic-based entropy loss. Code is available at https://github.com/shermanlian/spatial-entropy-loss.