# SDDM: Score-Decomposed Diffusion Models on Manifolds for Unpaired Image-to-Image Translation

arXiv: https://arxiv.org/abs/2308.02154 · HTML: https://mlsanity.com/paper/2308.02154/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [DualGAN: Unsupervised Dual Learning for Image-to-Image Translation](https://mlsanity.com/paper/1704.02510/) (2017)
- [Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1808.00948/) (2018)
- [Learning to Discover Cross-Domain Relations with Generative Adversarial Networks](https://mlsanity.com/paper/1703.05192/) (2017)
- [U-GAT-IT: Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation](https://mlsanity.com/paper/1907.10830/) (2019)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [Image-to-Image Translation: Methods and Applications](https://mlsanity.com/paper/2101.08629/) (2021)
- [Geometry-Consistent Generative Adversarial Networks for One-Sided Unsupervised Domain Mapping](https://mlsanity.com/paper/1809.05852/) (2018)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [One-Sided Unsupervised Domain Mapping](https://mlsanity.com/paper/1706.00826/) (2017)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)

## Built on by (most cited first, 14 of 14)

- [CycleDiff: Cycle Diffusion Models for Unpaired Image-to-image Translation](https://mlsanity.com/paper/2508.06625/) (2025)
- [Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillation](https://mlsanity.com/paper/2503.15056/) (2025)
- [Exploring the Design Space of Diffusion Bridge Models](https://mlsanity.com/paper/2410.21553/) (2024)
- [Contrastive Learning and Cycle Consistency-based Transductive Transfer Learning for Target Annotation](https://mlsanity.com/paper/2401.12340/) (2024)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
- [Learning to Match Unpaired Data with Minimum Entropy Coupling](https://mlsanity.com/paper/2503.08501/) (2025)
- [Latent Guidance in Diffusion Models for Perceptual Evaluations](https://mlsanity.com/paper/2506.00327/) (2025)
- [PRISM: Distribution-Gated Flow Matching for Controllable Unpaired Image Translation](https://mlsanity.com/paper/2608.06240/) (2026)
- [RL-I2IT: Image-to-Image Translation with Deep Reinforcement Learning](https://mlsanity.com/paper/2309.13672/) (2023)
- [Contrastive-SDE: Guiding Stochastic Differential Equations with Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2510.03821/) (2025)
- [TAG: Tangential Amplifying Guidance for Hallucination-Resistant Sampling](https://mlsanity.com/paper/2510.04533/) (2025)
- [GeoEdit: Local Frames for Fast, Training-Free On-Manifold Editing in Diffusion Models](https://mlsanity.com/paper/2604.24238/) (2026)
- [Source-Agnostic Image Translation Based on Latent Aware Adaptive Masking](https://mlsanity.com/paper/2608.14046/) (2026)
- [MaDeL: Manifold-Decomposed Feature Losses for Generative Modeling](https://mlsanity.com/paper/2610.04419/) (2026)

## Abstract (arXiv)

Recent score-based diffusion models (SBDMs) show promising results in unpaired image-to-image translation (I2I). However, existing methods, either energy-based or statistically-based, provide no explicit form of the interfered intermediate generative distributions. This work presents a new score-decomposed diffusion model (SDDM) on manifolds to explicitly optimize the tangled distributions during image generation. SDDM derives manifolds to make the distributions of adjacent time steps separable and decompose the score function or energy guidance into an image ``denoising" part and a content ``refinement" part. To refine the image in the same noise level, we equalize the refinement parts of the score function and energy guidance, which permits multi-objective optimization on the manifold. We also leverage the block adaptive instance normalization module to construct manifolds with lower dimensions but still concentrated with the perturbed reference image. SDDM outperforms existing SBDM-based methods with much fewer diffusion steps on several I2I benchmarks.