Spoken Language Understanding (SLU) is a critical component of voice assistants; it consists of converting speech to semantic parses for task execution. Previous works have explored end-to-end models to improve the quality and robustness of SLU models with Deliberation, however these models have remained autoregressive, resulting in higher latencies. In this work we introduce PRoDeliberation, a novel method leveraging a Connectionist Temporal Classification-based decoding strategy as well as a denoising objective to train robust non-autoregressive deliberation models. We show that PRoDeliberation achieves the latency reduction of parallel decoding (2-10x improvement over autoregressive models) while retaining the ability to correct Automatic Speech Recognition (ASR) mistranscriptions of autoregressive deliberation systems. We further show that the design of the denoising training allows PRoDeliberation to overcome the limitations of small ASR devices, and we provide analysis on the necessity of each component of the system.