In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the simulation of measurement-induced quantum phenomena. In particular, we focus on the measurement-altered quantum criticality protocol and generate local reduced density matrices of the critical chain given random measurement results. Such generation is enabled by a physics-preserving conditional diffusion generative model, which learns an observation-indexed probability distribution of an ensemble of quantum states, and then samples from that distribution given an observation.