  Diffusion models have been successfully adapted to text generation tasks by
mapping the discrete text into the continuous space. However, there exist
nonnegligible gaps between training and inference, owing to the absence of the
forward process during inference. Thus, the model only predicts based on the
previously generated reverse noise rather than the noise computed by the
forward process. Besides, the widely-used downsampling strategy in speeding up
the inference will cause the mismatch of diffusion trajectories between
training and inference. To understand and mitigate the above two types of
training-inference discrepancies, we launch a thorough preliminary study. Based
on our observations, we propose two simple yet effective methods to bridge the
gaps mentioned above, named Distance Penalty and Adaptive Decay Sampling.
Extensive experiments on \textbf{6} generation tasks confirm the superiority of
our methods, which can achieve $100\times \rightarrow 200\times$ speedup with
better performance.
