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..
Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptive
Authors: Tyler Farghly, Peter Potaptchik, Samuel Howard, George Deligiannidis, Jakiw Pidstrigach
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This work provides evidence for this conjecture, focusing on how such phenomena could result from the formulation of the learning problem through score matching. We inspect the role of implicit regularisation by investigating the effect of smoothing minimisers of the empirical score matching objective. Our theoretical and empirical results confirm that smoothing the score function or equivalently, smoothing in the log-density domain produces smoothing tangential to the data manifold. 5 High-dimensional experiments So far, our experiments have focused on illustrative low-dimensional settings to complement our theory. In this section, we consider higher-dimensional settings to investigate the extent to which the identified phenomena persist in scenarios more representative of practical applications. |
| Researcher Affiliation | Academia | Tyler Farghly Department of Statistics University of Oxford Peter Potaptchik Department of Statistics University of Oxford Samuel Howard Department of Statistics University of Oxford George Deligiannidis Department of Statistics University of Oxford Jakiw Pidstrigach Department of Statistics University of Oxford Correspondence to {last name}@stats.ox.ac.uk |
| Pseudocode | No | The paper describes algorithms and methods in textual form and through mathematical equations, but it does not include any explicitly labeled pseudocode blocks or algorithms with a structured, code-like format. |
| Open Source Code | Yes | Code to reproduce the experiments is available at https://github.com/samuel-howard/log_smoothing. |
| Open Datasets | Yes | We begin with MNIST and define a 32-dimensional VAE latent space (following Rombach et al. (2022)). Licenses: MNIST digits classification dataset (Le Cun et al., 2010), CC BY-SA 3.0 License |
| Dataset Splits | Yes | This ground-truth manifold is approximated using all samples of the digit 4, from which we use a subset of 100 samples as our training dataset. For a visualisation of the manifold, see Appendix G.3. We use η = 0.2, and use 16 equally spaced points along the curve as the training dataset. We use the decodings of 10 equidistant points along the latent triangular interpolation to define the training dataset. |
| Hardware Specification | No | The paper does not explicitly mention any specific hardware (e.g., GPU models, CPU models, or cloud computing instances with specifications) used for running the experiments. |
| Software Dependencies | No | The paper mentions using Python for code (Appendix G.4) and specific optimizers like Adam (Kingma and Ba, 2015), but does not provide version numbers for any libraries or software components used in the experiments. |
| Experiment Setup | Yes | VAE We train the VAE on 10,000 samples from the MNIST database. The VAE uses 16 initial feature channels, with scaling multiples of (1, 2, 2, 2) during downsampling, a convolutional kernel size of 3, a dropout rate of 0.1, and 4 groups for group normalisation. It is trained for 10,000 training steps with a batch size of 64, using the Adam optimiser (Kingma and Ba, 2015) with learning rate 1e-3 and default parameters 0.9, 0.999. Experiment hyperparameters We use a variance-exploding diffusion model with T = 9.0, a geometric noise schedule, and 100 generation steps with an Euler-Maruyama discretisation scheme. |