Objective: A new method for fitting diffusion-weighted magnetic resonance imaging (DW-MRI) data composed of an unknown number of multi-exponential components is presented and evaluated. Methods: The auto-regressive discrete acquisition points transformation (ADAPT) method is an adaption of the auto-regressive moving average system, which allows for the modeling of multi-exponential data and enables the estimation of the number of exponential components without prior assumptions. ADAPT was evaluated on simulated DW-MRI data. The optimum ADAPT fit was then applied to human brain DWI data and the correlation between the ADAPT coefficients and the parameters of the commonly used bi-exponential intravoxel incoherent motion (IVIM) method were investigated. Results: The ADAPT method can correctly identify the number of components and model the exponential data. The ADAPT coefficients were found to have strong correlations with the IVIM parameters. ADAPT(1,1)-β0 correlated with IVIM-D: ρ = 0.708, P <; 0.001. ADAPT(1,1)-α1 correlated with IVIM-f: ρ = 0.667, P <; 0.001. ADAPT(1,1)-β1 correlated with IVIM-D * : ρ = 0.741, P <; 0.001). Conclusion: ADAPT provides a method that can identify the number of exponential components in DWI data without prior assumptions, and determine potential complex diffusion biomarkers. Significance: ADAPT has the potential to provide a generalized fitting method for discrete multi-exponential data, and determine meaningful coefficients without prior information.