Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.
Runyu Zhang, Jiawei Zhang, Gioele Zardini et al.· 0 citations
Autonomous computer-use agents are increasingly applied to long-horizon tasks requiring coordinated application calls, persistent state tracking, and verifier-sensitive writes, yet they remain prone to procedural failures: misreading application state, tool semantics, or task progress. Procedural memory promises more consistent decisions and less redundant exploration, but constructing high-quality memory without model training remains challenging. We introduce CONTRAMEM, a source-flexible, training-free framework for self-evolving procedural memory that treats same-task outcome variation as supervision: differences in correctness, efficiency, recovery, and failure modes expose outcome-relevant procedural distinctions, distilled into a compact bank of app-level Function Cards and task-level Skill Cards that evolves through localized curation rather than append-only accumulation or whole-bank rewriting. On held-out GAIA2/ARE computer-use tasks, CONTRAMEM more than doubles the success rate across the three source-model targets (26.2% to 55.3%), with consistent per-model gains (GPT-5.5: 27.5 to 61.0; Claude Sonnet 4.6: 28.0 to 52.5; DeepSeek V4 Pro: 23.0 to 52.5). The same bank transfers unchanged to the unseen Qwen3.7 Plus (18.5 to 35.5), indicating transferable procedural knowledge rather than model-specific behavior. The same construction carries over unchanged to AppWorld, beating both no memory and its own single-source self-memory variant for all three mid-tier agents on both public test splits. Under a matched trajectory budget, heterogeneous multi-model trajectories yield stronger memory than self- or same-model multi-rollout memory: the margin comes from contrastive behavioral diversity, not stronger source agents or more sampling.
Zheyuan Deng, B.-L. Lu, Hanqi Feng et al.· 0 citations