PickMoment: Continuous-Time Single-Image-to-Video via Learning Deblurring and Blur-to-Video

Motion blur arises from the temporal integration of a continuous sharp signal over a finite exposure window, yet existing learning-based methods sidestep this physical model and predict only the sharp signal itself: most single-image deblurring methods recover a single frame at the exposure center, while blur-to-video methods predict a fixed set of frames. We introduce PickMoment, a continuous-time reformulation that directly learns the interval-mean blur over arbitrary sub-intervals of the exposure with a single deterministic model. Drawing an analogy to MeanFlow's average-velocity formulation, we train the model with three supervisions derived from the blur integral: an empirical reconstruction loss from available subframes, an additivity loss that enforces self-consistency across overlapping sub-intervals, and a sharp-frame loss anchored at the zero-interval limit. A single trained model unifies single-image deblurring, blur-to-video generation, and continuous-time pick-a-moment recovery as different queries to the same network, with no separate training for each task. Our PickMoment achieves state-of-the-art performance among generative-based deblurring methods on GoPro and HIDE while competitive against restoration-based methods on RealBlur, and the highest per-frame fidelity on GoPro-7 blur-to-video, all in a single forward pass without iterative sampling.