Mountainous terrains evolve over geological timescales through erosion processes driven by the complex interplay of transported quantities such as water, sediment, and rockfall. A key challenge in erosion modeling is the simultaneous simulation of transport and erosive processes, which differ in temporal scales by several orders of magnitude. We address this challenge with a novel, parallel, stochastic particle-based method capable of simulating transport over geological timescales. Our approach relaxes the strong assumptions on velocity required by prior works ( e.g. , based on the Stream Power Law), enabling a new erosion model grounded in a more general form of momentum conservation. We demonstrate that our scheme accurately solves the underlying conservation laws and avoids artifacts common in previous works. Furthermore, we show that our new erosion model captures multiscale geomorphological features, producing coherent basin structures and dynamic phenomena such as braided rivers, meanders, and deltas.