State-of-the-art man-made shape generative models usually adopt established generative models under a suitable implicit shape representation. A common theme is to perform distribution alignment, which does not explicitly model important shape priors. As a result, many synthetic shapes are not connected. Other synthetic shapes present problems of physical stability and geometric feasibility. This paper introduces a novel latent diffusion shape-generative model guided by a quality check that outputs a score of a latent code. The scoring function employs a learned function that provides a geometric feasibility score and a deterministic procedure to quantify a physical stability score. The key to our approach is a new diffusion procedure that combines the discrete empirical data distribution and a continuous distribution induced by the quality checker. We introduce a principled approach to determine the tradeoff parameters for learning the denoising network at different noise levels. We also present an efficient strategy that avoids evaluating the score for each synthetic shape during the optimization procedure. Experimental results show that our approach outperforms state-of-the-art shape generations quantitatively and qualitatively on ShapeNet-v2.