arXiv:2603.03412v1 Announce Type: cross Abstract: Recent advances in generative image editing have enabled transformative applications, from professional head shot generation to avatar stylization. However, these systems often require uploading high-fidelity facial images to third-party models, raising concerns around biometric privacy, data misuse, and user consent. We propose a privacy-preserving pipeline that supports high-quality editing while keeping users in control over their biometric data in face-centric use cases. Our approach separates identity-sensitive regions from editable image context using on-device segmentation and masking, enabling secure, user-controlled editing without modifying third-party generative models. Unlike traditional cloud-based tools, PRIVATEEDIT enforces privacy by default: biometric data is never exposed or transmitted. This design requires no access to or retraining of third-party models, making it compatible with a wide range of commercial APIs. By treating privacy as a core design constraint, our system supports responsible generative AI centered on user autonomy and trust. The pipeline includes a tunable masking mechanism that lets users control how much facial information is concealed, allowing them to balance privacy and output fidelity based on trust level or use case. We demonstrate its applicability in professional and creative workflows and provide a user interface for selective anonymization. By advocating privacy-by-design in generative AI, our work offers both technical feasibility and normative guidance for protecting digital identity. The source code is available at https://github.com/Dipeshtamboli/PrivateEdit-Privacy-Preserving-GenAI.

arXiv:2602.13506v1 Announce Type: cross Abstract: Optimizing monotone non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class of such functions. This condition provides a powerful unifying framework, strictly generalizing both DR-submodular functions and One-Sided Smooth (OSS) functions. Our central theoretical contribution demonstrates that $\gamma$-weakly $\theta$-up-concave functions are upper-linearizable: for any feasible point, we can construct a linear surrogate whose gains provably approximate the original non-linear objective. This approximation holds up to a constant factor, namely the approximation coefficient, dependent solely on $\gamma$, $\theta$, and the geometry of the feasible set. This linearizability yields immediate and unified approximation guarantees for a wide range of problems. Specifically, we obtain unified approximation guarantees for offline optimization as well as static and dynamic regret bounds in online settings via standard reductions to linear optimization. Moreover, our framework recovers the optimal approximation coefficient for DR-submodular maximization and significantly improves existing approximation coefficients for OSS optimization, particularly over matroid constraints.

arXiv:2510.10854v2 Announce Type: replace-cross Abstract: 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 $\widetilde{\mathcal{O}}(\epsilon^{-2})$. 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.