The rapid integration of generative artificial intelligence (AI) into judicial and quasi-judicial decision-making processes has transformed traditional understandings of procedural fairness, accountability, and legal legitimacy. While existing AI governance frameworks increasingly address transparency, risk management, and human oversight, they remain fragmented and insufficient to safeguard due process rights in transnational legal environments. This study examines how contemporary regulatory regimes respond to the procedural and human rights challenges posed by generative AI and evaluates their capacity to ensure judicial accountability across jurisdictions. Employing a comparative socio-legal mixed-methods approach, the study analyzes regulatory instruments and governance frameworks in the European Union, the United States, Canada, and Singapore, complemented by doctrinal legal analysis and comparative policy evaluation. The findings reveal substantial regulatory inconsistencies regarding explainability, contestability, algorithmic auditing, human oversight, and cross-border accountability. Existing frameworks continue to prioritize risk management while providing limited procedural safeguards for individuals affected by AI-assisted adjudicative systems. In response, this article develops a Human Rights-Centered Transnational Algorithmic Due Process Model that integrates explainability, contestability, human oversight, algorithmic auditability, human rights impact assessment, and cross-border accountability into a unified governance architecture. The study contributes to contemporary debates on AI governance by reconceptualizing algorithmic due process as a transnational legal principle capable of strengthening judicial accountability and protecting fundamental rights in the era of generative AI.