We present MELLE, a novel continuous-valued token based language modeling approach for text-to-speech synthesis (TTS). MELLE autoregressively generates continuous mel-spectrogram frames directly from text condition, bypassing the need for vector quantization, which is typically designed for audio compression and sacrifices fidelity compared to continuous representations. Specifically, (i) instead of cross-entropy loss, we apply regression loss with a proposed spectrogram flux loss function to model the probability distribution of the continuous-valued tokens; (ii) we have incorporated variational inference into MELLE to facilitate sampling mechanisms, thereby enhancing the output diversity and model robustness. Experiments demonstrate that, compared to the two-stage codec language model VALL-E and its variants, the single-stage MELLE mitigates robustness issues by avoiding the inherent flaws of sampling vector-quantized codes, achieves superior performance across multiple metrics, and, most importantly, offers a more streamlined paradigm. The demos of our work are provided at https://aka.ms/melle.