Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Efficient Diffusion Models for Symmetric Manifolds
Authors: Oren Mangoubi, Neil He, Nisheeth K. Vishnoi
ICML 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirically, our model outperforms prior methods in training speed and improves sample quality on synthetic datasets on the torus, special orthogonal group, and unitary group. |
| Researcher Affiliation | Academia | 1Worcester Polytechnic Institute, USA. 2Yale University, USA. |
| Pseudocode | Yes | We present a new training algorithm (Algorithm 1) for these manifolds, achieving per-iteration runtimes of O(d) arithmetic operations... We also provide a sampling algorithm (Algorithm 2) with guarantees on accuracy and runtime. Algorithm 1 Training algorithm Algorithm 2 Sampling algorithm |
| Open Source Code | Yes | Our code can be found at github.com/mangoubi/Efficient-Diffusion-Models-for-Symmetric-Manifolds |
| Open Datasets | No | Empirically, our model outperforms prior methods in training speed and improves sample quality on synthetic datasets on the torus, special orthogonal group, and unitary group. For the torus Td, following several works (De Bortoli et al., 2022; Zhu et al., 2025), we train diffusion models on data sampled from wrapped Gaussians on tori of different dimensions d {2, 10, 50, 100, 1000}, with mean 0 and covariance 0.2Id (See Appendix C.1 for definition of wrapped Gaussian). For U(n), following (Zhu et al., 2025), we use a dataset on U(n) of unitary matrices representing time-evolution operators eit H of a quantum oscillator. For SO(n), following (Zhu et al., 2025), we use datasets sampled from a mixture of a small number k of wrapped Gaussians on SO(n). |
| Dataset Splits | Yes | A total of 30,000 points were sampled as the training dataset, and 10,000 were sampled as a test dataset to compute the log-likelihood of the generative model outputs. We then sample 40,000 matrices from the wrapped Gaussian mixture distribution on SO(n) with means m1, m2 and covariance 0.2Id. 30,000 of these matrices are used for training, and the remaining 10,000 matrices comprise the test dataset used to evaluate the C2ST score of the generative model outputs. |
| Hardware Specification | Yes | Simulations evaluating sample quality on the Torus were run on an Apple M1 chip with 10 cores. Simulations on the special orthogonal group and unitary group were run on a single RTX 3070. All simulations evaluating per-iteration training runtime were run on a single RTX 3070 as well. |
| Software Dependencies | No | The paper mentions training neural networks but does not specify any software versions for libraries or frameworks used (e.g., Python, PyTorch, TensorFlow, CUDA). |
| Experiment Setup | Yes | For the torus, the neural network architecture consists of a 4-layer MLP with a hidden dimension of k, with a sin activation function. We set k = 512 for d < 1000 and k = 2048 for d = 1000. The models were trained with a batch size of 512, with an appropriate variance scheduler. For each model, we trained the neural networks for 50K iterations when d < 1000, and for 100K iterations when d = 1000. In the case of the special orthogonal group, the neural network architecture consists of a 4-layer MLP with a hidden dimension k = 512, with a sin activation function. For each model, the neural networks were trained for 100K iterations, with a batch size of 512, and an appropriate variance scheduler. For both the drift and diffusion terms, let (Xi, ti) be inputs into the neural network... In our simulations, we set k = 8 and D = 512. For each model, the neural networks were trained for 80K iterations, with a batch size of 512, and an appropriate variance scheduler. |