Lung cancer is the leading cause of cancer-related mortality worldwide, largely because most patients are diagnosed at advanced stages. Low-Dose Computed Tomography (LDCT) is the standard screening modality, where lung cancer in its earliest stages typically manifests as a pulmonary nodule. When a suspicious nodule is identified, patients undergo repeated CT scans over time, and radiologists compare successive images to assess growth. However, manual evaluation of subtle temporal changes is time-consuming, prone to error, and difficult to quantify robustly. AI-based tools capable of automatically detecting nodules and forecasting their evolution could substantially improve clinical decision-making. NoduleFlow is designed as a biologically-informed AI framework that automatically identifies suspicious lung nodules in CT scans and forecasts their future appearance over time. Unlike existing approaches, which are predominantly data-driven and vulnerable to data scarcity and poor generalisation, NoduleFlow will integrate imaging features extracted from CT scans with prior knowledge encoded in established biological models of tumour growth, specifically the Gompertz growth law. Development will proceed in three stages: (1) lung cancer nodules' volume and mass prediction with uncertainty quantification; (2) nodules' shape forecasting via biologically conditioned diffusion; (3) nodules' texture generation and full appearance synthesis. The project will use publicly available datasets comprising LDCT scans of lung cancer patients. The computational demands are driven by training and evaluating 3D AI diffusion models and Physically-Informed Neural Networks (PINNs) on volumetric CT data. Specifically, the project requires: (1) training diffusion-based generative models conditioned on 3D CT volumes for nodule shape and texture forecasting; (2) training PINNs with Gompertz-constrained loss functions across patient-specific growth trajectories; (3) joint optimisation of the full pipeline (PINN + diffusion) with uncertainty propagation; (4) systematic benchmarking against state-of-the-art approaches across both datasets; and (5) hyperparameter search and ablation studies to quantify the added value of biological conditioning versus purely data-driven baselines. NoduleFlow introduces several key advances over the state of the art. It will be the first framework to employ a PINN for lung nodule evolution prediction. Moreover, it will be the first to apply diffusion-based generative models to this task, where all existing approaches rely on autoencoders, spatial transformation networks, or GAN-like architectures. Finally, it will be the first approach in this field to provide quantified uncertainty estimates alongside its predictions. Providing calibrated confidence alongside each forecast transforms the model from a black-box predictor into a decision-support tool that clinicians can act on. NoduleFlow will enable clinicians to distinguish high-confidence predictions from cases requiring closer follow-up, supporting more personalised and evidence-based lung cancer management.