The Diffusion Decision Model (DDM) is widely used in binary decision tasks, breaking down response times into meaningful psychological parameters. However, DDM has limitations, particularly in cases of fast errors under speed instructions. The model incorporates additional across-trial variability parameters to explain fast errors which are hard to recover. In contrast, the Levy Flights model (Voss et al., 2019) addresses fast errors with jumps in evidence accumulation which can occur in first miliseconds of decision process. Introducing the stability parameter, alpha, this model is suggested to better capture human decision-making. We propose that in cases where the true data-generating model is Levy Flights, DDM may introduce biases during interpretation. A preliminary study in the project using fast-dm (Voss & Voss, 2007) revealed a systematic bias against threshold separation and non-decision time parameters. To further investigate, we conducted a simulation study via Bayesflow (Radev et al., 2020), training 4 separate networks with standard and full models for a parameter recovery study. That indicated DDM's parameter recovery was not healthy when data comes from Levy Flights. Our ongoing goal is to provide a comprehensive picture of the possible bias against Levy flights model in Diffusion model framework.