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Discrete Diffusion Models are Minimax Optimal Under Sparsity
Luca Blunda, Tyler Farghly, Umut Simsekli +1
Discrete diffusion models have emerged as a leading alternative to autoregressive models for generating text and other categorical data, yet their theoretical foundations remain le…
Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling
Federica Milinanni, Tyler Farghly, Jun Yang
Sampling from high-dimensional, heavy-tailed distributions is a fundamental challenge in computational statistics, as many standard Markov chain Monte Carlo (MCMC) methods mix poor…
Tightening the Score Matching Gap for Diffusion Models
Benjamin Dupuis, Tyler Farghly, Maxime Haddouche +2
Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lo…
Benign Overfitting Does Not Occur in Diffusion Models
Tyler Farghly, Benjamin Dupuis, Alain Durmus +1
Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good genera…
Metropolis-Adjusted Diffusion Models
Kevin H. Lam, Tyler Farghly, Christopher Williams +3
Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to a…
On-Average Stability of Multipass Preconditioned SGD and Effective Dimension
Simon Vary, Tyler Farghly, Ilja Kuzborskij +1
We study trade-offs between the population risk curvature, geometry of the noise, and preconditioning on the generalisation ability of the multipass Preconditioned Stochastic Gradi…