Faults are crucial subsurface features that significantly influence the mechanical behavior and hydraulic properties of rock masses. Interpreting them from seismic data may lead to various scenarios due to uncertainties arising from limited seismic bandwidth and possible imaging errors. Although methods addressing fault uncertainty exist, only a few of them can produce curved and sub-seismic faults at once while quantitatively honoring seismic images and avoiding anchoring in a reference interpretation. In this work, we use a mathematical framework of marked point processes to approximate fault networks in two dimensions with a set of line segments. The proposed stochastic model, namely Candy Model, incorporates simple pairwise and nearby connections to capture the interactions between fault segments. The novelty of this approach lies in conditioning the stochastic model using input image of fault probabilities generated by a Convolutional Neural Network (CNN). The Metropolis-Hastings algorithm is used to generate various scenarios of fault network configurations, thereby exploring the model space associated with the Candy Model and reflecting the uncertainty. Probability level sets constructed from these fault segment configurations provide insights on the obtained realizations and on the model parameters. The empty space function produces a ranking of the generated fault networks against an existing interpretation by testing and quantifying their spatial variability. The approach is applied on two-dimensional sections of seismic data, acquired in the Central North Sea.