Liver cancer is among the leading causes of cancer-related deaths worldwide. Accurate delineation of hepatic tumors is crucial for diagnosis, prognosis, and treatment planning, yet manual annotation is labor-intensive and subject to variability. Deep neural networks (DNNs) have shown promise in automating segmentation but require large amounts of high-quality labeled data, which is difficult to obtain. Incorporating noisy labels without proper handling can corrupt training and degrade performance.We introduce MPVT+, a noise-robust training framework that integrates a pixel-wise noise-adaptation module with a multi-stage perturbation and variable-teacher (MPVT) consistency strategy. The noise adaptor infers corruption probabilities and re-weights unreliable supervision, while MPVT assembles an ensemble of stochastic teacher models that apply progressively stringent perturbations. This combination enables the network to exploit both clean and noisy labels without overfitting.Experiments conducted on 739 retrospectively collected liver-tumor CT datasets demonstrated that MPVT+ significantly outperformed baseline and traditional noise-handling approaches. Compared to a noise-free U-Net baseline (Dice Similarity Coefficient [DSC] 75.1%), MPVT+ improved segmentation accuracy to 80.3%. The framework consistently achieved superior results across multiple evaluation metrics, including DSC, JSC, SVD, and VOE.The MPVT+ framework demonstrates that principled noise modeling, coupled with consistency training, effectively unlocks the potential of imperfect medical datasets. This strategy reduces the dependency on perfectly labeled datasets and moves fully automated liver tumor delineation closer to clinical applicability.Copyright © 2025 Cheng, Tian, Zhou, Xie, Gong, Liu, Wei and Lu.