Abstract
<title>Abstract</title> <p>Virtual Try-On (VTO) systems have emerged as a cornerstone of modern e-commerce, bridging the gap between digital retail and physical fitting experiences. However, existing image- and diffusion-based VTO frameworks experience severe degradation in visual fidelity, spatial alignment, and structural consistency when subjected to dynamic environmental uncertainties, such as non-uniform illumination shifts, unconstrained user poses, and multi-layer garment occlusions. This paper addresses these limitations by establishing a rigorous mathematical framework for VTO optimization under uncertainty. We model the VTO generation pipeline as a Distributionally Robust Optimization (DRO) problem over ambiguity sets defined by optimal transport metrics. We propose the Robust Stochastic Variance-Reduced Virtual Try-On (RSVR-VTO) algorithm, a novel optimization framework that guarantees stable geometric warping and texture synthesis under bounded perturbations. We provide comprehensive theoretical analyses proving that RSVR-VTO achieves an \(\:O(1/\epsilon\:²)\) convergence rate to a first-order stationary point under non-convex, L-smooth conditions. Furthermore, we derive explicit generalization error bounds demonstrating that our performance guarantees scale gracefully with the complexity of environmental noise. Extensive empirical evaluations on high-resolution benchmarks (VITON-HD and DressCode) validate our theoretical findings, showing that the proposed framework consistently outperforms state-of-the-art approaches in structural coherence and perceptual metrics under severe environmental perturbations. Dynamic uncertainties are successfully mitigated. The official PyTorch implementation of the RSVR-VTO algorithm, along with reproducible cluster execution logs, is publicly available at https://github.com/elhamr1997/RSVR-VTO.git</p>