5 papers
Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models
Marcos Tapia Costa, Nikolas Kantas, George Deligiannidis
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed…
Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptive
Tyler Farghly, Peter Potaptchik, Samuel Howard +2
Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these…
Beyond Real Data: Synthetic Data through the Lens of Regularization
Amitis Shidani, Tyler Farghly, Yang Sun +2
Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we prese…
Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis
Tyler Farghly, Patrick Rebeschini, George Deligiannidis +1
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown…
Mixing Time Bounds for the Gibbs Sampler under Isoperimetry
Alexander Goyal, George Deligiannidis, Nikolas Kantas
We establish bounds on the conductance for the systematic-scan and random-scan Gibbs samplers when the target distribution satisfies a Poincaré or log-Sobolev inequality and posses…