Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization
Authors: Joe Benton, Valentin De Bortoli, Arnaud Doucet, George Deligiannidis
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distribution. We show that diffusion models require at most O( d log2(1/δ) ε2 ) steps to approximate an arbitrary distribution on Rd corrupted with Gaussian noise of variance δ to within ε2 in KL divergence. Our proof extends the Girsanov-based methods of previous works. We introduce a refined treatment of the error from discretizing the reverse SDE inspired by stochastic localization. |
| Researcher Affiliation | Academia | Department of Statistics, University of Oxford, {benton,doucet,deligian}@stats.ox.ac.uk CNRS, ENS Ulm, Paris, valentin.debortoli@gmail.com |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the described methodology. |
| Open Datasets | No | This is a theoretical paper that focuses on mathematical proofs and convergence bounds, and does not involve empirical studies with datasets. Therefore, it does not provide information about public datasets. |
| Dataset Splits | No | This is a theoretical paper that focuses on mathematical proofs and convergence bounds, and does not involve empirical studies with dataset splits. |
| Hardware Specification | No | This is a theoretical paper focusing on mathematical proofs and convergence bounds, and does not describe any hardware specifications for running experiments. |
| Software Dependencies | No | This is a theoretical paper focusing on mathematical proofs and convergence bounds, and does not describe any specific software dependencies with version numbers for experimental replication. |
| Experiment Setup | No | This is a theoretical paper focusing on mathematical proofs and convergence bounds, and does not describe specific experimental setup details like hyperparameters or training configurations. |