MethaneSAT was a spaceborne imaging spectrometer that observed column-averaged dry-air mole fractions of methane (XCH<sub>4</sub>) in the atmosphere from March 2024 to June 2025. The data have fine spatial resolution (110 m x 400 m at nadir), high precision (~3 ppb at 2 km x 2 km aggregation) and wide swath (220 km at nadir). The goal of MethaneSAT is to provide comprehensive emissions characterization for oil and gas production regions, spanning the gap between area flux mappers and point source imagers. In this paper we introduce the MethaneSAT FLEXPART Inverse Model (MFIM), an inverse modeling framework for quantifying total emissions and their spatial distribution from MethaneSAT observations. We use a Lagrangian particle dispersion model, the FLEXible PARTicle dispersion model (FLEXPART v.11), in time reversed mode to determine the influence of surface emissions on atmospheric concentrations across a MethaneSAT scene (aggregated to 0.02° x 0.02° resolution). We then obtain the optimum emissions field using a Hamiltonian Monte Carlo (HMC) sampler to solve the inverse problem. We apply the inversion system to 9 scenes from the Permian Basin, yielding an annual emission rate of 3.49 ±1.43 Tg/yr (398 ±163 tons/hr). Emission estimates from MFIM resolve high emitting regions within the basin without the use of a spatially informed prior. MFIM leverages the strengths of the MethaneSAT observing system (10<sup>4</sup> independent observations) to produce spatially explicit, high-resolution (0.05° x 0.05°) emission estimates for application to monitoring and mitigation of methane emissions. Our results compare well to the MethaneSAT Level 4 product from the operational CORE (Column Observations to Regional Emissions) inversion algorithm, as well as other top-down studies in the region, lending confidence that regional methane flux estimates from MethaneSAT are robust against differences in modeled transport.