In some steep valleys, flood-induced changes in river bed elevation pose significantly greater risks to infrastructure than floodwaters alone. Over the short term, the river may aggrade or degrade by several meters during a single flood. Whereas floodwaters recede after each event, moreover, riverbed changes add up over successive floods. To quantify the resulting geomorphic risk and its evolution over time, we propose in this paper a new stochastic model of river bed elevation change. The bed is assumed to rise and drop according to a random walk, driven by the composition of two gamma processes that respectively pace the hydrologic forcing and the geomorphic response. The model can therefore incorporate various sources of uncertainty, associated with precipitation and debris flow activity within the contributing watershed. To test the model, we apply it to a highly active montane river, the Laonong River in southwestern Taiwan. Model calibration is achieved from a combination of long and short term data, including radiocarbon-dated deposits and modern river records. The modelled distributions fit the data well, including the likelihood of extreme changes. The model also produces a reasonable hindcast of the geomorphic damage suffered over the last ten years by Highway 20, a vulnerable road link sited along the river, and can be used to forecast future geomorphic risk.