Fig. 3: Comparison with tumor synthesis methods and CT foundation models.

a–l The 5-fold cross-validation results of 12 public datasets. Box plots show the mean (center), 25th and 75th percentiles (bounds of box), and minima to maxima (whiskers). SynTumor³⁸ and DiffTumor⁴⁶ are two tumor synthesis methods using the same segmentation model⁵¹ as FreeTumor, while SynTumor³⁸ is only applicable to liver tumors, and DiffTumor⁴⁶ is not applicable to lung tumors and COVID-19. We use a “cross mark” (xmark) to signify that this method is not applicable to this dataset. For example, the “cross mark” in (d) means SynTumor³⁸ is not applicable to the pancreas tumor dataset MSD07¹⁰. In addition, MAE3D⁵², SwinSSL⁵³, and VoCo⁵⁴ are three CT foundation models based on self-supervised learning. The same segmentation model⁵¹ is adopted for fair comparisons. Overall, on 12 public datasets, FreeTumor surpasses the best-competing method by an average of 5.1% in Dice scores (two-sided paired t test p-values = 3.786 × 10^-5, remaining significant after Bonferroni correction72 for multiple comparisons, α = 0.00417, 3.786 × 10^-5 <  0.00417). m–r Out-of-domain evaluation. The standard deviations are obtained from five experiments. Overall, in 6 out-of-domain experiments, FreeTumor surpasses the best-competing method by average 7.9% Dice scores (two-sided paired t test p-values  = 3.735 × 10⁻³, remaining significant after Bonferroni correction⁷² for multiple comparisons, α = 0.00833, 3.735 × 10⁻³ < 0.00833.) in out-of-domain evaluation. Detailed results are presented in Supplementary Tables 9, 10, and 11. Source data are provided as a Source Data file.