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The study of hand-object interaction requires generating viable grasp poses for high-dimensional multi-finger models, often relying on analytic grasp synthesis which tends to produce brittle and unnatural results. This paper presents Grasp'D, an approach for grasp synthesis with a differentiable contact simulation from both known models as well as visual inputs. We use gradient-based methods as an alternative to sampling-based grasp synthesis, which fails without simplifying assumptions, such as pre-specified contact locations and eigengrasps. Such assumptions limit grasp discovery and, in particular, exclude high-contact power grasps. In contrast, our simulation-based approach allows for stable, efficient, physically realistic, high-contact grasp synthesis, even for gripper morphologies with high-degrees of freedom. We identify and address challenges in making grasp simulation amenable to gradient-based optimization, such as non-smooth object surface geometry, contact sparsity, and a rugged optimization landscape. Grasp'D compares favorably to analytic grasp synthesis on human and robotic hand models, and resultant grasps achieve over 4x denser contact, leading to significantly higher grasp stability. Video and code available at https://graspd-eccv22.github.io/.