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..
A solvable model of learning generative diffusion: theory and insights
Authors: Hugo Cui, Cengiz Pehlevan, Yue Lu
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The theoretical predictions further quantitatively capture experiments on simple real datasets. Figure 1: Evolution of the summary statistics Mτ, Qτ and of the skip connection strength bτ as a function of the training time τ, for σ = tanh, r = 2, pt = 0, αt = 1 t, βt = t, G = {1/2}. The target density is a trimodal Gaussian mixture ρ = 1/3N(µ1, Id)+1/3N(µ2, Id)+1/3N(µ3, Id). Solid lines: numerical experiments in dimension d = 1000. Dashed: theoretical characterization (10) of Result 2.1. |
| Researcher Affiliation | Academia | Hugo Cui Center of Mathematical Sciences and Applications, Harvard University Cengiz Pehlevan Center for Brain Science, Kempner Institute for the Study of Natural and Artificial Intelligence, John A. Paulson School of Engineering and Applied Sciences, Harvard University Yue M Lu John A. Paulson School of Engineering and Applied Sciences, Center of Mathematical Sciences and Applications, Harvard University |
| Pseudocode | No | The paper describes mathematical derivations and theoretical characterizations but does not include any pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code employed in this manuscript is accessible on this online repository. The code is provided in the supplementary material, and will be released on a public online repository upon de-anonymization. |
| Open Datasets | Yes | Example 2 MNIST In Fig. 3, a DAE-parametrized generative model with r = 2 hidden units and σ = tanh activation is trained to generate a Gaussian distribution with covariance matching that of MNIST sevens [39]. For completeness, we report in Fig. 10 in Appendix D an additional experiment on the Fashion MNIST [87] dataset of clothing item images. |
| Dataset Splits | No | The paper discusses using "the total MNIST training set" and subsets of Fashion MNIST as target densities, but does not provide explicit training/validation/test splits for the generative model's learning process or evaluation. |
| Hardware Specification | No | The present manuscript is theoretical in nature, and all the experiments are very small in scale and simply run on a personal laptop. |
| Software Dependencies | No | The paper mentions using the scipy [78] implementation of Gaussian kernel density estimation (KDE) but does not specify its version number or other software dependencies with specific versions. |
| Experiment Setup | Yes | Parameters σ = tanh, r = 2, λ = 0, η = 0.2, G = {1/2} were used, and the target density ρ was taken to be a Gaussian mixture with three isotropic clusters... The weight vectors were initialized along the centroids of the target density, with norm 0.1, while the initial skip connection strength is b0 = 0. In all the figures, the sampling was carried out by discretizing the interval (0, 1) in N steps tk = 1/N for k J0, NK, and running the discretized SDE (98) in experiments, and the associated theoretical characterization of Results B.1 and 2.3 for the theoretical predictions, up to a stopping time 0 tf 1. In Fig. 7, N = 100, tf = 0.95; in Fig. 8, N = 100, tf = 0.98 and in Figs. 3,?? and 4, N = 50, tf = 0.98. |