Deterministic transmission plays a vital role in industrial networks. The time-sensitive network (TSN) protocol family offers a promising paradigm for transmitting time-critical data. To achieve low latency and high Quality of Service (QoS) in TSN, appropriate data flow scheduling is needed under the given network topology and data flow requirements to fully utilize the potential of TSN. Both time-triggered flows and sporadic flows can carry high-priority data and need to be considered jointly to eliminate the effects of each other. To this end, in this work, we investigate the challenging mixed-flow scheduling problem and propose a novel diffusion-based algorithm, DiffTSN, to solve the joint routing and scheduling problem of mixed flows. We transform the sporadic flows into probabilistic flows and design certain mechanisms to fit the nature of these probabilistic flows. For routing, we transform the problem into a diffusion policy and constraint denoising process with a value guide to achieve a better routing policy. For scheduling, we adopt a first-valid-time-slot algorithm to determine the start transmission time of the flows. We train and evaluate DiffTSN in our TSN simulator. Experiments show that DiffTSN outperforms state-of-the-art algorithms in various metrics.