Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the precise measurement in computer networks because of the high measurement cost, and the unavoidable transmission loss. Although some methods proposed in recent years allowed estimating network traffic from partial flow-level or link-level measurements, they often perform poorly for traffic matrix estimation nowadays. Despite strong assumptions like low-rank structure and the prior distribution, existing techniques are usually task-specific and tend to be significantly worse as modern network communication is extremely complicated and dynamic. To address the dilemma, this paper proposed a diffusion-based traffic matrix analysis framework named Diffusion-TM, which leverages problem-agnostic diffusion to notably elevate the estimation performance in both traffic distribution and accuracy. The novel framework not only takes advantage of the powerful generative ability of diffusion models to produce realistic network traffic, but also leverages the denoising process to unbiasedly estimate all end-to-end traffic in a plug-and-play manner under theoretical guarantee. Moreover, taking into account that compiling an intact traffic dataset is usually infeasible, we also propose a two-stage training scheme to make our framework be insensitive to missing values in the dataset. With extensive experiments with real-world datasets, we illustrate the effectiveness of Diffusion-TM on several tasks. Moreover, the results also demonstrate that our method can obtain promising results even with $5\%$ known values left in the datasets.