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Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion

arXiv · AI, language, vision and robotics · article · Aug 30, 2026 · UTC

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 ac

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