TopoDiffusionNet: A Topology-aware Diffusion Model
Saumya Gupta, Dimitris Samaras, Chao Chen
TL;DR
TopoDiffusionNet introduces a novel method that integrates topological data analysis with diffusion models to ensure generated images maintain specified topological structures, enhancing their utility in precise applications.
Contribution
It is the first to incorporate topology constraints into diffusion models using persistent homology, enabling control over image topology during generation.
Findings
Significant improvements in topological accuracy across four datasets.
First integration of topology with diffusion models.
Effective preservation of desired structures during denoising.
Abstract
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…
Peer Reviews
Decision·ICLR 2025 Poster
The posed problem is interesting, and it is relevant for a wide community. Defining new ways to control generation and especially incorporating this knowledge into the diffusion process itself provide interesting insights. The paper is also informative and well-organized: The text is well-written, and it is pretty straightforward. The proposed methodology is clear, and the figures are quite insightful. Experiments consider diverse datasets and control results are convincing.
My main concern is that the paper does not offer much insight into the trade-off between control and quality. It is pretty natural to wonder how the control impacts the quality of the generation compared with other methods. The qualitative examples shown seem ok, but it is also evident that the quality is quite degraded compared to alternatives -- this might be a cause of the generative 2D ControlNet itself or that the control does not incorporate enough domain knowledge and provide a mask diffi
Maintaining desired compositionality is a key challenge for diffusion models, and getting a model to output the desired quantity of discrete objects is often difficult. Framing this problem through the lens of persistent homology makes a lot of sense and ties nicely to the difficulty of dealing with noisy samples at intermediate timesteps. Additionally, being able to condition on first homology is also a nice feature, albeit it seems a bit more contrived (and indeed the main demonstrated use cas
My main concerns with this paper have to do with the overall novelty as well as the overall justification for the approach. While this paper is indeed the first to consider diffusion-based image generation through the lens of TDA and persistent homology, the actual machinery proposed to accomplish this is very similar to prior work that combines TDA with deep learning --- a key insight is differentiating through the persistence computation, but this is not unique to the diffusion setting. I do
I am not an expert in image generation, but I like the idea of adding topological constraints to image generation. It could be very interesting to be able to accurately control resulting images' topology. I found the approach to be rather straightforward and thus easy to understand and implement. Considering I could not find a prior work that aims to achieve the same result, I find this approach novel.
Again, I am not an expert in image generation, however it seems to me that in the end, the paper focuses mainly on number of objects and less so on more important topological invariants such as connectivity. There are many interesting tests one could cook up, e.g., choose Betti numbers that force a very specific topology (double annulus) and show the method can achieve that. These more interesting topological invariants are also not directly measured in the quantitative evaluations, as far as I
Code & Models
Videos
Taxonomy
TopicsNeural Networks and Applications · Music and Audio Processing
MethodsTemporaral Difference Network · Diffusion