Not yet reviewed by Pith; the record is open.

We experimentally demonstrate a new class of optomechanical nonlinearities in weakly damped micromechanical resonators, arising from the interplay between the Duffing nonlinearity, intermodal coupling, and thermal fluctuations. Within the bistable regime of a single Duffing mode driven by radiation pressure forces, we observe stochastically generated sidebands, originating from thermal fluctuations around equilibrium trajectories in phase space, and exploit these sidebands to induce probabilistic transitions between bistable states using weak secondary acoustic excitation. Extending this framework to multimodal interactions, we show that nonlinear modes coupling within the same resonator leads to similar transitions due to parametric modulation around the noise-excited sidebands as a result of frequency mixing. Simultaneously, abrupt changes in displacements of modes cause their instantaneous energy exchange rates to span five orders of magnitude. These findings open new avenues for reconfigurable optomechanical networks, nonreciprocal energy transport, and precision sensing based on dynamically tunable mechanical nonlinearities.