The logarithm of the flow of a river in Quebec, Canada, is modeled as a Gaussian diffusion process. Using this model, forecasts of the river flow are made for up to 7 days ahead. The forecasts are found to be much more accurate for 1 day ahead than those produced by a deterministic model called PREVIS. The stochastic model also outperforms PREVIS for 2 days ahead forecasts and is comparable to PREVIS for 3 days ahead forecasts. In general, PREVIS is more accurate than the stochastic model proposed from 4 days ahead forecasts. Various possible improvements of the stochastic model are considered, including the incorporation of exogenous variables and the use of linear regression. The best forecasts are actually obtained by taking the average value of the forecasts produced by the stochastic model and by PREVIS. Finally, confidence interval for the forecasted values are also provided.