The expected atmospheric signal when performing exoplanet transit spectroscopy, especially for terrestrial planets, is measured in a few tens of parts per million. The technique is thus very sensitive to various sources of noise. This is particularly true when using the Single Object Slitless Spectroscopy (SOSS) mode on the NIRISS instrument aboard the JWST, given the wide spectral traces of its images. Current methods to deal with 1/f (correlated) noise leave residuals that are almost double that of the expected readout noise. Here, we explore the use of Score-Based Models (SBM) to learn the distribution of noise in dark SOSS images, which we then use as a likelihood model in the Scored-based Likelihood Characterization (SLIC) framework to produce posterior samples of the underlying (noiseless) spectral traces. We aim to apply this method to time series spectroscopic observations, potentially reducing our error to the photon noise limit. This could substantially improve our signal-to-noise by up to a factor of two for some spectral regions and thus enable higher precision transit spectroscopy.