arXiv Machine Learning
DDPM Score Matching and Distribution Learning
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arXiv Machine Learning
Sep 11
Generalized Score Matching for Parameter Estimation on Convex Domains
The paper introduces a generalized score matching objective for parameter estimation on convex subsets of ρ^d, derived from Minimum Probability Flow learning. It shows that this objective is a proper local scoring rule of second order, ensuring recovery of the true density when minimized, and proves convexity and consistency for exponential family models under standard conditions. Experiments demonstrate the method’s effectiveness on constrained domains where the partition function is intractable, including a generative modeling use‑case.
arXiv Machine Learning
Jun 19
Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence
arXiv:2606. 19876v1 Announce Type: new Abstract: The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems.
arXiv Machine Learning
Aug 5
Heteroscedasticity of Denoising Score Matching with Generalised Smooth Noise
arXiv:2508. 01597v2 Announce Type: replace Abstract: Score Matching (SM) is a powerful framework for estimating the log-density derivatives of a distribution without calculating its normalizing constants.
arXiv Machine Learning
Jul 20
Diffusion models recover accurate mixture weights despite score function insensitivity
arXiv:2607. 15485v1 Announce Type: new Abstract: Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative mode amplitudes, which can be interpreted as mixture weights.
arXiv Machine Learning
Aug 20
Diffusion Models for High-Dimensional Clustered Data: Intrinsic-Dimension Adaptivity via Bayesian Classification
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv Machine Learning
Jun 9
Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.