Xu, Brendel, Prinn, and Habets developed a method for completing room impulse responses by conditioning a diffusion model on physically simulated early reflections. The direct path and first few bounces are computed geometrically using the image-source method, which is exact but limited to simple reflection orders. The diffusion model then generates the late reverberation tail — the dense, chaotic decay that carries the room's timbral character. A key design choice was imposing no fixed duration constraint on the early-reflection input, allowing the handoff between physics and statistics to occur wherever the geometry stops being tractable.
The through-claim is that a room's acoustic identity lives in two incommensurable regimes, and no single method can represent both. Early reflections are sparse and geometrically determined: each bounce corresponds to a specific wall at a specific distance, producing discrete arrivals that can be exactly computed. Late reverberation is dense and statistical: hundreds of overlapping paths merge into a smooth decay whose character depends on aggregate surface absorption, not individual reflections. The system works precisely because it uses geometry where geometry applies and statistics where statistics apply, with the boundary determined by the physics rather than by computational convenience.
This two-regime structure recurs in any system where a deterministic origin gives way to a stochastic steady state. Epidemic models: the first few transmission events are traceable; the community spread phase is statistical. Stock prices: the initial response to news is deterministic; the subsequent price discovery is diffusive. The right model is not a compromise between exactness and approximation — it is exact methods applied to their regime and approximate methods applied to theirs, with an honest boundary between them.
(arXiv:2603.12442)