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Because of bright starlight leakage in coronagraphic raw images, faint astrophysical objects such as exoplanets can only be detected using powerful point spread function (PSF) subtraction algorithms. However, these algorithms have strong effects on faint objects of interest, and often prevent precise spectroscopic analysis and scattering property measurements of circumstellar disks. For this reason, PSF-subtraction effects is currently the main limitations to the precise characterization of exoplanetary dust with scattered-light imaging. Forward-modeling techniques have long been developed for point source objects. However, forward-modeling with disks is complicated by the fact that the disk cannot be simplified using a simple point source convolved by the PSF as the astrophysical model; all hypothetical disk morphologies must be explored to understand the subtle and non-linear effects of the PSF subtraction algorithm on the shape and local geometry of these systems. Because of their complex geometries, the forward-modeling process has to be repeated tens or hundred of thousands of times on disks with slightly different physical properties. All of these geometries are then compared to the PSF-subtracted image of the data, within an MCMC or a Chi-square wrapper. In this paper, we present here DiskFM, a new open-source algorithm included in the PSF subtraction algorithms package pyKLIP. This code allows to produce fast forward-modeling for a variety of observation strategies (ADI, SDI, ADI+SDI, RDI). pyKLIP has already been used for SPHERE/IRDIS and GPI data. It is readily available on all instruments supported by pyKLIP (SPHERE/IFS, SCExAO/CHARIS), and can be quickly adapted for other coronagraphic instruments.