UltraDiff: Differentiable Ray Tracing in Ultrasound for Shape Optimization

Physically-based differentiable rendering enables gradient-based optimization of scene parameters by matching rendered images to measurements, but has so far mainly focused on light transport. We extend this paradigm to medical ultrasound, where image formation resembles transient rendering: echoes are binned by time-of-flight rather than projected onto an image plane. We present UltraDiff, a modular framework for differentiable ultrasound ray tracing. UltraDiff formulates ultrasound image formation as a path-space integral, gated by travel time between the transducer and tissue interfaces, and derives a Monte Carlo estimator of both the forward model and its gradients with respect to scene parameters. We demonstrate this on an inverse geometry estimation: starting from a sphere, an SDF is optimized until simulated echoes match measured ones, recovering vertebral surfaces from simulated B-mode sweeps and from a real robotic acquisition of a spine phantom. Unlike state-of-the-art ultrasound shape reconstruction methods, which rely on pre-segmented images, our approach operates unsupervised on B-mode images through analysis-by-synthesis, while achieving competitive geometric accuracy. Implemented on top of Mitsuba 3, UltraDiff brings differentiable path tracing to a new sensing modality and provides a foundation for inverse problems in acoustic imaging.