  The development of X-ray Free Electron Lasers (XFELs) has opened numerous
opportunities to probe atomic structure and ultrafast dynamics of various
materials. Single Particle Imaging (SPI) with XFELs enables the investigation
of biological particles in their natural physiological states with unparalleled
temporal resolution, while circumventing the need for cryogenic conditions or
crystallization. However, reconstructing real-space structures from
reciprocal-space x-ray diffraction data is highly challenging due to the
absence of phase and orientation information, which is further complicated by
weak scattering signals and considerable fluctuations in the number of photons
per pulse. In this work, we present an end-to-end, self-supervised machine
learning approach to recover particle orientations and estimate reciprocal
space intensities from diffraction images only. Our method demonstrates great
robustness under demanding experimental conditions with significantly enhanced
reconstruction capabilities compared with conventional algorithms, and
signifies a paradigm shift in SPI as currently practiced at XFELs.
