摘要： Aiming at the problem that the existing multivariate time series prediction methods based on diffusion model have insufficient conditional information representation ability and large computational cost of long sequence modeling, this paper proposes a diffusion model (Wavelet-Conditioned Diffusion Model with Mamba, WCDM-M) that combines wavelet condition enhancement and lightweight Mamba architecture. The wavelet conditional enhancement network is designed in the WCDM-M model. The multi-scale time-frequency analysis of the historical time series is carried out by continuous wavelet transform, and the periodicity, local variation and transient characteristics at different time positions and scales are expressed explicitly. Then, using the convolutional coding structure composed of two layers of InceptionV1 modules, the time-frequency features under different receptive fields are extracted through multi-scale convolution kernels and pooling branches, and the scale dimension is compressed through deep convolution. The conditional vector is generated by linear mapping, which provides a multi-scale time-frequency prior for the diffusion reverse denoising process. In the denoising network, a lightweight time-series modeling backbone based on the selective state space model Mamba is designed. By removing the Conv1D module in the native Mamba, the linear mapping is used to simplify the redundant projection, and the L-Mamba module is constructed to achieve efficient modeling of long-distance timing dependencies. At the same time, the wavelet condition vector and diffusion step are embedded into the joint input multi-layer perceptron to generate feature scaling and offset parameters, and the adaptive feature modulation of different diffusion stages is realized by the condition layer normalization mechanism. Experimental verification is performed on five public time-series datasets of ETTm1, Electricity, Traffic, Weather and Exchange. The results show that in the 96-step prediction task, the MSE of WCDM-M on the five datasets is 0.3212,0.1767,0.4196,0.0071 and 0.0410, respectively, which is better than the optimal results in the corresponding comparison model. Among them, the MSE of the Weather dataset is reduced to 0.0071, indicating that the model can effectively capture high-frequency fluctuation pattern; the MSE of the Exchange data set reaches 0.0410, which verifies the predictive capability of the model for non-stationary time series. The results of ablation experiments show that after removing the wavelet conditional network, the average MSE of all data sets and prediction lengths is increased by 26.4%; after using single-scale wavelet or removing Inception multi-branch coding, the average MSE is increased by 15.1% and 10.5% respectively, which proves that multi-scale time-frequency conditions and multi-receptive field feature extraction play an important role in model performance improvement. In addition, the WCDM-M parameter is 11.2M, which is lower than 18.5M of the Transformer denoising version WCDM-T, and the single-round training time is 89.7ms, which is 26.6% lower than WCDM-T. The WCDM-M model combines the wavelet time-frequency condition enhancement with the lightweight Mamba denoising network, which reduces the computational complexity and improves the prediction ability of the diffusion model for periodic changes, local mutations and non-stationary dynamic patterns. It provides an effective method for the prediction of complex and variable time series with both accuracy and efficiency.