We propose Stochastic Interpolant Prior for Speech (SIPS), a plug-and-play framework for speech enhancement and separation that augments pretrained predictors with a generative clean speech prior. Building on stochastic interpolants, we decompose the sampling dynamics into a predictor-induced drift and a score-based denoising component. The predictor guides sampling toward a task-consistent estimate, while a score model trained exclusively on clean speech promotes perceptual naturalness. Unlike prior hybrid approaches, which typically rely on architecture-specific conditioning and are tied to particular predictors or degradation settings, SIPS employs a degradation-agnostic prior that can be reused across predictors and additive degradation tasks without retraining. We evaluate SIPS on speech enhancement and separation using recent predictors such as SEMamba and FlexIO. Across both tasks, SIPS consistently improves non-intrusive speech quality metrics while maintaining competitive performance on reference-based distortion measures and word error rate. For speech enhancement, these improvements are further supported by a subjective listening test.

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