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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Guided Diffusion Sampling on Function Spaces with Applications to PDEs
Authors: Jiachen Yao, Abbas Mammadov, Julius Berner, Gavin Kerrigan, Jong Chul Ye, Kamyar Azizzadenesheli, Animashree Anandkumar
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability and speedup. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/Fun DPS. |
| Researcher Affiliation | Collaboration | Jiachen Yao , Abbas Mammadov California Institute of Technology Julius Berner NVIDIA Gavin Kerrigan University of Oxford Jong Chul Ye KAIST Kamyar Azizzadenesheli NVIDIA Anima Anandkumar California Institute of Technology |
| Pseudocode | Yes | Algorithm 1 Fun DPS Training (Training an unconditional diffusion model in function spaces) Require: Data distribution µ, GRF prior covariance C, noise-level distribution p(σ) 1: Initialize model parameters θ 2: repeat 3: a µ, σ p(σ) {Draw clean function and noise level} 4: η N(0, σ2C) {Sample GRF noise} 5: y a + η {Construct noisy sample} 6: ˆa Dθ(y, σ) {Compute denoised prediction} 7: L λ(σ) ˆa a 2 H {Compute training loss} 8: Update parameters θ by minimizing L 9: until converged 10: return Dθ |
| Open Source Code | Yes | Code is available at https://github.com/neuraloperator/Fun DPS. |
| Open Datasets | Yes | Datasets have been taken from Diffusion PDE s work, which is openly available. |
| Dataset Splits | Yes | We follow the same strategy as in Diffusion PDE [17] to generate datasets, where we prepare 50,000 training samples and 1,000 test samples for each PDE. The Navier-Stokes equation with boundary conditions specifically consists of 14,000 train and 1,000 test samples. |
| Hardware Specification | Yes | Regarding the actual run time, our model averages 15s/sample for 500 steps (without multi-resolution inference technique) on a single NVIDIA RTX 4090 GPU, while Diffusion PDE takes 190s/sample for 2000 steps on the same hardware and the same 128 128 discretization. |
| Software Dependencies | No | The paper mentions using EDM-FS [61] and a neural operator architecture [52]. However, it does not provide specific version numbers for key software components such as programming languages, libraries, or frameworks (e.g., Python, PyTorch, CUDA versions). |
| Experiment Setup | Yes | The hyperparameters we used for training and inference are listed in Table 3. Hyperparameter Value learning_rate 0.0001 learning_rate_warmup 5 million samples ema_half_life 0.5 million samples dropout 0.13 rbf_scale 0.05 sigma_max 80 sigma_min 0.002 rho 7 |