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Identifying cancer driver genes (CDGs) remains a central challenge in cancer genomics, as frequency-based mutation approaches often miss rare but functionally important regulators. We present PICDGI, a computational framework that predicts driver-like regulatory genes by integrating dynamic gene-gene interaction modeling with single-cell RNA sequencing (scRNA-seq) data. Rather than relying on DNA mutation calls, PICDGI infers functional driver activity from time-resolved expression patterns and latent regulatory influence among genes during tumor progression. Methodologically, PICDGI employs a time-varying state-space model with variational Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling to estimate evolving gene interaction effects. The posterior distributions capture both the magnitude and uncertainty of each gene's inferred regulatory influence. From these, PICDGI derives a driver coefficient that quantifies the strength and reliability of each gene's contribution to progression-associated expression dynamics, enabling the prioritization of impactful regulators over neutral passengers. Applied to lung adenocarcinoma (LUAD) scRNA-seq data, PICDGI recovered known oncogenes and tumor suppressors and nominated novel candidate drivers, including JPH1 and CHEK1, which are implicated in calcium signaling, mitochondrial regulation, and DNA repair. These genes exhibit trajectory-aligned activity consistent with tumor evolution and immune-modulatory processes. Comparative analysis using Moran's I statistics in Monocle 3 showed that PICDGI-prioritized genes display stronger progression-associated dynamics than genes selected by spatial autocorrelation alone. We further validated PICDGI on an independent pediatric acute myeloid leukemia (AML) scRNA-seq cohort, where it consistently recovered known drivers and relapse-associated regulatory programs under fixed model parameters. By integrating interaction-informed dynamic modeling with single-cell resolution data, PICDGI provides a generalizable and biologically grounded framework for identifying rare and context-specific regulatory drivers of cancer progression, with broad applicability across tumor types.