This paper introduces a framework for probabilistic forecasting of dynamical systems using generative modeling. The approach leverages stochastic interpolants to construct a generative model between an arbitrary base distribution and the target distribution. A fictitious, non-physical stochastic dynamics is designed to produce samples from the target conditional distribution in finite time and without bias. This process maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. The drift coefficient of the stochastic differential equation (SDE) is shown to be non-singular and can be learned efficiently via square loss regression. The drift and diffusion coefficients of the SDE can be adjusted after training, and a specific choice that minimizes the impact of estimation error gives a Föllmer process. The method is validated on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes equations and video prediction on the KTH and CLEVRER datasets. The approach is shown to produce diverse samples consistent with the conditional distribution of interest and outperforms deterministic forecasting methods. The method is also effective for video generation tasks, where it produces more accurate results than standard conditional generative modeling. The framework is implemented using stochastic differential equations and allows for autoregressive forecasting without retraining. The results demonstrate the effectiveness of the approach in capturing the probabilistic nature of complex systems and provide a new perspective on Föllmer processes. The method is applicable to a wide range of forecasting tasks and has the potential to be used in empirical weather data and other domains where physical structure needs to be incorporated into the generative model.This paper introduces a framework for probabilistic forecasting of dynamical systems using generative modeling. The approach leverages stochastic interpolants to construct a generative model between an arbitrary base distribution and the target distribution. A fictitious, non-physical stochastic dynamics is designed to produce samples from the target conditional distribution in finite time and without bias. This process maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. The drift coefficient of the stochastic differential equation (SDE) is shown to be non-singular and can be learned efficiently via square loss regression. The drift and diffusion coefficients of the SDE can be adjusted after training, and a specific choice that minimizes the impact of estimation error gives a Föllmer process. The method is validated on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes equations and video prediction on the KTH and CLEVRER datasets. The approach is shown to produce diverse samples consistent with the conditional distribution of interest and outperforms deterministic forecasting methods. The method is also effective for video generation tasks, where it produces more accurate results than standard conditional generative modeling. The framework is implemented using stochastic differential equations and allows for autoregressive forecasting without retraining. The results demonstrate the effectiveness of the approach in capturing the probabilistic nature of complex systems and provide a new perspective on Föllmer processes. The method is applicable to a wide range of forecasting tasks and has the potential to be used in empirical weather data and other domains where physical structure needs to be incorporated into the generative model.