I don't like the sound of this...
Table 1 on Page 994 (page 6 of the PDF)
A significant increase of benign neoplastic lesions was observed for rats and mice in a long-term NTP study. However, malignant tumors were not significantly increased compared to the control groups. Moreover, there was a lack of dose-dependent effects as well as consistency across sexes and/or species. Previously, it was concluded by JECFA that curcumin was not genotoxic. However, new in vitro and in vivo studies gave positive results (e.g. DNA adducts and chromosomal aberrations). According to EFSA ‘the available in vivo genotoxicity studies were insufficient to eliminate the concerns regarding genotoxicity’. Nevertheless, there is no carcinogenicity.
Not exactly a ringing endorsement.