<p>Deep Generative models have shown impressive capabilities in several applications, e.g., image, video, and audio synthesis. Importantly, they can infer probability distributions from data implicitly. For this reason, they have promising applications in learning stochastic dynamics, with potential applications in computational condensed matter physics and materials science. Indeed, random thermal fluctuations have a key role in several phenomena, such as surface roughening, nucleation, crystal growth, and phase transitions. Here we provide a comprehensive dataset of trajectories of one of such systems, i.e., the progressive roughening of monoatomic steps on top of a simple cubic (100) surface. The system has been simulated with a Kinetic Monte Carlo approach, implementing the edge diffusion conditions. Among other characteristics, this system is convenient because its dynamics can be represented as a series of binary images, with white and black pixels corresponding to occupied and unoccupied surface sites, respectively. The repository contains 3 KMC datasets composed of 300 independent trajectories each. Every trajectory contains 1000 subsequent states. The datasets differ in the initial condition (one flat stripe and one undulated one on a 64x64 computational cell) and the domain size (one undulated stripe on a 72x64 computational cell). Evolutions predicted by a Generative Adversarial Network approach trained on the flat stripe dataset are also provided, serving as a benchmark for comparing alternative implementations on the same problem. These comprise the evolution of flat profiles on domains of different lengths (32, 48, 64, 72, 80, 96, and 128) to the equilibrium value and relaxation dynamics from undulated profiles conformal to those used in the KMC datasets. </p>