The Drift-Diffusion Model (DDM) has become one of the most influential computational frameworks for understanding human decision-making, with its application expanding steadily from cognitive psychology into social psychology, behavioral economics, cognitive neuroscience, and psychiatry. As the most representative model within the Evidence Accumulation Model (EAM) framework, the DDM allows researchers to decompose behavioral data into parameters that may be interpreted as cognitive proccesses. However, few papers provide a whole picture of DDM's mathematical foundations, parameter estimation algorithms, available software, and principled parameter interpretation.

Here we present a systematic introduction of the DDM across three interconnected levels. The mathematical principles of DDM, Wiener diffusion process, trace back to discrete random walk processes in statistics. Researchers applied Wiener process in the context of a decision-making and developed Wiener First Passage Time (WFPT) distribution, the statistical model of DDM, to model reaction times. DDM also used as cognitive model or measurement model where its parameters was interpreted as psychological processes, e.g., drift rate is interpreted as the rate of evidence accumulation. However, these interpretations only hold when model assumptions are meet. In short, DDM should be viewed as an application of mathematical to a specific field and its parameters are not inherently related to psychological processes. As a model, DDM can both generate synthetic data and fit real data to estimate possible parameters. Off-shelf software, including frequentist tools (e.g., fast-dm) and Bayesian tools (e.g., HDDM), allow researcher to do so easily.

Based on the understanding of DDM, we suggested two principled pathways for applying the DDM in empirical research. When researchers' theoretical assumptions are aligned with the DDM, researchers should translate theoretical assumptions into parameter constraints, construct candidate models in which only theoretically relevant parameters vary across conditions, and select the optimal model through model comparison and posterior predictive checks. When task design violates the standard DDM's premises, researchers should instead adopt an extension or customization pathway: identifying the violated assumption, modifying the generative mechanism, constructing an expanded parameter set, and validating the extension through model comparison and posterior predictive checks. The Shrinking Spotlight Model (SSP) exemplifies this extension pathway by incorporating a time-varying.

We conclude that the psychological meaning of DDM parameters hinges on the alignment between the model's theoretical assumptions and experimental task design. Researchers should interpret the parameters of DDM with caution: only when task structure and theoretical premises are consistent with the model's core assumptions can the DDM transcend its role as a statistical model and function as a genuine cognitive model. This logic applies not only to the standard DDM, but also underlies model extension and customization: regardless of which pathway is adopted, alignment between theoretical assumptions and model premises remains the prerequisite for psychologically meaningful parameter interpretation.

This paper is of interest for researchers may apply evidence accumulation models to their data. A better understanding the three-level structure of the DDM prevents common misuses such as misinterpretation of parameters from misspecified models. Moreover, we cautioned whether the standard DDM is sufficient or whether task-specific extensions are warranted. Finally, we listed software that beyond standard DDM, such as PyDDM, HSSM, providing practical resources for researchers with psychology background.