# TopoDiffusionNet: A Topology-aware Diffusion Model

arXiv: https://arxiv.org/abs/2410.16646 · HTML: https://mlsanity.com/paper/2410.16646/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 57 of its 79 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 57)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [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)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)
- [GLIGEN: Open-Set Grounded Text-to-Image Generation](https://mlsanity.com/paper/2301.07093/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [Uni-ControlNet: All-in-One Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16322/) (2023)
- [Training-Free Layout Control with Cross-Attention Guidance](https://mlsanity.com/paper/2304.03373/) (2023)
- [Composer: Creative and Controllable Image Synthesis with Composable Conditions](https://mlsanity.com/paper/2302.09778/) (2023)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)

## Built on by (most cited first, 10 of 10)

- [TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Model](https://mlsanity.com/paper/2412.06011/) (2024)
- [BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesis](https://mlsanity.com/paper/2504.04532/) (2025)
- [TPIE: Topology-Preserved Image Editing With Text Instructions](https://mlsanity.com/paper/2411.16714/) (2024)
- [Anatomy-DT: A Cross-Diffusion Digital Twin for Anatomical Evolution](https://mlsanity.com/paper/2509.25280/) (2025)
- [A Dual-Mode ViT-Conditioned Diffusion Framework with an Adaptive Conditioning Bridge for Breast Cancer Segmentation](https://mlsanity.com/paper/2511.05989/) (2025)
- [Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models](https://mlsanity.com/paper/2511.20587/) (2025)
- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)
- [PFlow-T: A Persistence-Driven Forward Process for Topology-Controlled Generation](https://mlsanity.com/paper/2605.17555/) (2026)
- [Geodesic-informed Generative Diffusion Model For Topology-preserved Image Video Generation](https://mlsanity.com/paper/2609.08153/) (2026)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Diffusion models excel at creating visually impressive images but often struggle to generate images with a specified topology. The Betti number, which represents the number of structures in an image, is a fundamental measure in topology. Yet, diffusion models fail to satisfy even this basic constraint. This limitation restricts their utility in applications requiring exact control, like robotics and environmental modeling. To address this, we propose TopoDiffusionNet (TDN), a novel approach that enforces diffusion models to maintain the desired topology. We leverage tools from topological data analysis, particularly persistent homology, to extract the topological structures within an image. We then design a topology-based objective function to guide the denoising process, preserving intended structures while suppressing noisy ones. Our experiments across four datasets demonstrate significant improvements in topological accuracy. TDN is the first to integrate topology with diffusion models, opening new avenues of research in this area. Code available at https://github.com/Saumya-Gupta-26/TopoDiffusionNet