  Metal halides perovskites (MHPs) are attracting considerable interest for
optoelectronic applications, with Cs$_2$AgBiBr$_6$ one of the main contenders
among lead-free systems. Cs$_2$AgBiBr$_6$ crystallizes in a nominally
double-perovskite structure, but exhibits a soft lattice with large atomic
fluctuations characteristic of MHPs. While crucial to understand
electron-phonon and phonon-phonon couplings, the spatio-temporal correlations
of these fluctuations remain largely unknown. Here, we reveal these
correlations using comprehensive neutron and x-ray scattering measurements on
Cs$_2$AgBiBr$_6$ single-crystals, complemented with first-principles
simulations augmented with machine-learned neural-network potentials. We report
the discovery of an unexpected complex modulated ground state structure
containing several hundred atoms, arising from a soft-phonon instability of the
low-temperature tetragonal phase. Further, our experiments and simulations both
reveal extensive correlated 2D fluctuations of Br octahedra at finite
temperature, arising from soft anharmonic optic phonons, reflecting very
shallow potential wells. These results provide new insights into the atomic
structure and fluctuations in MHPs, critical to understand and control their
thermal and optoelectronic properties.
