Efficient design of microstructures with targeted properties has always been a challenging task owing to the expensive and time-consuming nature of the problem. In recent years, generative models have been used to accelerate this process. However, most of these methods are hindered by the choice of their generative model - either due to stability and usability, like with GANs, or flexibility of the model itself, like the availability of a semantically meaningful latent space. We propose a diffusion autoencoder based generative design framework that not only provides the fidelity and stability benefits of diffusion models but also has a desirable latent space that can be exploited by evolutionary algorithms. We employ this framework to solve multiple simultaneous objectives to find a Pareto frontier of candidate microstructures. We also show that the search space of optimization can be drastically reduced by conditioning the model with target objective values. We demonstrate the efficacy of the proposed framework on a number of optimization and generative tasks based on two-phase morphology dataset derived from Cahn-Hilliard equations.