  Advanced accelerator-based light sources such as free electron lasers (FEL)
accelerate highly relativistic electron beams to generate incredibly short (10s
of femtoseconds) coherent flashes of light for dynamic imaging, whose
brightness exceeds that of traditional synchrotron-based light sources by
orders of magnitude. FEL operation requires precise control of the shape and
energy of the extremely short electron bunches whose characteristics directly
translate into the properties of the produced light. Control of short intense
beams is difficult due to beam characteristics drifting with time and complex
collective effects such as space charge and coherent synchrotron radiation.
Detailed diagnostics of beam properties are therefore essential for precise
beam control. Such measurements typically rely on a destructive approach based
on a combination of a transverse deflecting resonant cavity followed by a
dipole magnet in order to measure a beam's 2D time vs energy longitudinal
phase-space distribution. In this paper, we develop a non-invasive virtual
diagnostic of an electron beam's longitudinal phase space at megapixel
resolution (1024 x 1024) based on a generative conditional diffusion model. We
demonstrate the model's generative ability on experimental data from the
European X-ray FEL.
