arXiv subjects

Aadithya Srikanth

Publications and source records attributed to Aadithya Srikanth.

3 recordsLinked to original sources

arXiv2026

Minimax-Optimal Predictive Flow Matching under Distribution Drift

Flow matching learns a generative velocity field by regression, but under distribution drift a field must be deployed before the current data arrive. We study this predictive problem for a fixed, possibly nonconvex, neural class, with dynamic regret against the best represented field of each round. We propose DyProd-FM, which refits flow matching on dyadic historical prefixes and selects among the fits with a sleeping Prod master. Without knowing any drift budget, it attains regret $\widetilde{O}(\min\{N_ω+1,1+\sqrt{TΩ}\})$ in the relative velocity risk variation $Ω$ and $\widetilde{O}(\min\{N_μ+1,1+T^{1/3}V_μ^{2/3}\})$ in the target-law variation $V_μ=\sum_t W_2(μ_{t+1},μ_t)$, up to approximation and fitting costs. Matching lower bounds for fixed classes show that both rates are optimal in $T$ and in the budgets up to logarithmic factors. Prior optimal dynamic-regret guarantees rely on a convex decision set with strongly convex or exp-concave losses, whereas our class may be nonconvex and no curvature in its parameters is assumed. The target-law rate rests on a second-order link between the two variations, which the base noise of flow matching provides.

cs.LG↗

arXiv2026

Discrete State Diffusion Models: A Sample Complexity Perspective

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(ε^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.

cs.LG↗

arXiv2025

Insights into Closed-form IPM-GAN Discriminator Guidance for Diffusion Modeling

Diffusion models are a state-of-the-art generative modeling framework that transform noise to images via Langevin sampling, guided by the score, which is the gradient of the logarithm of the data distribution. Recent works have shown empirically that the generation quality can be improved when guided by classifier network, which is typically the discriminator trained in a generative adversarial network (GAN) setting. In this paper, we propose a theoretical framework to analyze the effect of the GAN discriminator on Langevin-based sampling, and show that the IPM-GAN optimization can be seen as one of smoothed score-matching, wherein the scores of the data and the generator distributions are convolved with the kernel function associated with the IPM. The proposed approach serves to unify score-based training and optimization of IPM-GANs. Based on these insights, we demonstrate that closed-form kernel-based discriminator guidance, results in improvements (in terms of CLIP-FID and KID metrics) when applied atop baseline diffusion models. We demonstrate these results on the denoising diffusion implicit model (DDIM) and latent diffusion model (LDM) settings on various standard datasets. We also show that the proposed approach can be combined with existing accelerated-diffusion techniques to improve latent-space image generation.

cs.LG↗