Diffusion models are important tools to investigate the processes underlying simple tasks. Common ways to estimate these models leverage the likelihood function (i.e., the probability of the parameters given the data). In this talk, we will present an approach to compute the exact gradients of the diffusion model with time-dependent parameters (as in many conflict task diffusion models), when it is formulated as either a differential or integral equation. Using these exact gradients enables a shift from commonly used derivative-free optimization methods like Nelder-Mead to more efficient gradient-based methods, such as Gradient Descent, BFGS, or Newton's method. These techniques significantly accelerate the parameter identification process. Additionally, they allow for more exact model diagnostics and statistical inference.