With recent technological advances, process logs, which were traditionally deterministic in nature, are being captured from non-deterministic sources, such as uncertain sensors or machine learning models (that predict activities using cameras). In the presence of stochastically-known logs, logs that contain probabilistic information, the need for stochastic trace recovery increases, to offer reliable means of understanding the processes that govern such systems. We design a novel deep learning approach for stochastic trace recovery, based on Diffusion Denoising Probabilistic Models (DDPM), which makes use of process knowledge (either implicitly by discovering a model or explicitly by injecting process knowledge in the training phase) to recover traces by denoising. We conduct an empirical evaluation demonstrating state-of-the-art performance with up to a $\mathbf{2 5 \%}$ improvement over existing methods, along with increased robustness under high noise levels.