Designing multi-phase, heterogeneous materials such as metal-ceramic composites, dual-phase steels, and polymer blends, which consist of elastoplastic phases with complex and varied property distributions, presents a high-dimensional design challenge. This work introduces a denoising diffusion algorithm to address this challenge by embedding the desired behaviors in a latent space. The algorithm utilizes denoising diffusion probabilistic models to refine microstructural designs iteratively, generating realistic samples with tailored mechanical responses. Reversing a Markov diffusion process, it efficiently manipulates the multi-phase topology and material parameters of microstructures, producing a diverse array of prototypes with targeted stiffness, yield surface responses, and hardening mechanisms. Neural network surrogates replace high-fidelity finite element simulations, enabling rapid identification of prototypes within the desired performance range. The results demonstrate the effectiveness of the denoising diffusion approach in generating microstructures with precisely tuned elastoplastic properties, all within the latent space informed by the training data. Numerical experiments validate the algorithm's capability in inverse design, providing insights into the intricate relationships between microstructural geometry, topology, and their resultant macroscopic elastoplastic behaviors.