  The chaotic nature of x-ray free-electron-laser pulses is a major bottleneck
that has limited the joint temporal and spectral resolution of spectroscopic
measurements. We show how to use the stochastic x-ray field statistics to
overcome this difficulty by correlation signals averaged over independent pulse
realizations. No control is required over the spectral phase of the pulse,
enabling immediate application with existing, noisy x-ray free-electron-laser
pulses. The proposed stimulated Raman technique provides the broad observation
bandwidth and high time-frequency resolution needed for the observation of
elementary molecular events. A model is used to simulate chaotic
free-electron-laser pulses and calculate their correlation properties. The
resulting joint temporal/spectral resolution is exemplified for a molecular
model system with time-dependent frequencies and for the RNA base Uracil
passing through a conical intersection. Ultrafast coherences, which represent a
direct signature of the nonadiabatic dynamics, are resolved. The detail and
depth of physical information accessed by the proposed stochastic signal are
virtually identical to those obtained by phase-controlled pulses.
