2026ApJ...999..186Z

We introduce TransFit-CSM, a fast and physically consistent framework for modeling interaction-powered transients. The method self-consistently couples the ejecta-circumstellar medium (CSM) shock dynamics to radiative diffusion from a moving heating boundary that is tied to the shocks. In this way, both the photon escape path and the effective diffusion time evolve with radius and time. We numerically solve the mass-momentum equations for the forward and reverse shocks together with the diffusion equation in the unshocked CSM. As a result, TransFit-CSM reproduces the canonical sequence of an early dark phase, a diffusion-mediated rise and peak, and a post-interaction cooling tail, and it clarifies why Arnett-like peak rules break down in optically thick CSM. The framework is Bayesian-ready and constrains physical parameters of the ejecta and CSM from bolometric or joint multiband light curves. Applications to SN 2006gy and SN 2010jl demonstrate accurate fits and physically interpretable posteriors. These fits highlight the dominant role of pre-supernova mass loss in shaping the observables. Because it is both computationally efficient and physically grounded, TransFit-CSM bridges simple analytic prescriptions and radiation-hydrodynamic simulations. This capability enables population-level inference for current and upcoming time-domain surveys.