Recently, Denoising Diffusion Probabilistic Models (DDPMs) have attained leading performances across a diverse range of generative tasks. However, in the field of speech synthesis, although DDPMs exhibit impressive performance, their prolonged training duration and substantial inference costs hinder practical deployment. Existing approaches primarily focus on enhancing inference speed, while approaches to accelerate training—a key factor in the costs associated with adding or customizing voices—often necessitate complex modifications to the model, compromising their universal applicability. To address the aforementioned challenges, we propose an inquiry: is it possible to enhance the training/inference speed and performance of DDPMs by modifying the speech signal itself? In this paper, we double the training and inference speed of Speech DDPMs by simply redirecting the generative target to the wavelet domain. This method not only achieves comparable or superior performance to the original model in speech synthesis tasks but also demonstrates its versatility. By investigating and utilizing different wavelet bases, our approach proves effective not just in speech synthesis, but also in speech enhancement.

Recent advances in large language models (LLMs) have promoted generative error correction (GER) for automatic speech recognition (ASR), which aims to predict the ground-truth transcription from the decoded N-best hypotheses. Thanks to the strong language generation ability of LLMs and rich information in the N-best list, GER shows great effectiveness in enhancing ASR results. However, it still suffers from two limitations: 1) LLMs are unaware of the source speech during GER, which may lead to results that are grammatically correct but violate the source speech content, 2) N-best hypotheses usually only vary in a few tokens, making it redundant to send all of them for GER, which could confuse LLM about which tokens to focus on and thus lead to increased miscorrection. In this paper, we propose ClozeGER, a new paradigm for ASR generative error correction. First, we introduce a multimodal LLM (i.e., SpeechGPT) to receive source speech as extra input to improve the fidelity of correction output. Then, we reformat GER as a cloze test with logits calibration to remove the input information redundancy and simplify GER with clear instructions. Experiments show that ClozeGER achieves a new breakthrough over vanilla GER on 9 popular ASR datasets.