Owing to the diversity of cancer types and the spatiotemporal heterogeneity of tumour signals, high-resolution imaging of occult malignancy is challenging. ¹⁸F-fluorodeoxyglucose positron emission tomography allows for near-universal cancer detection, yet in many clinical scenarios it is hampered by false positives. Here, we report a method for the amplification of imaging contrast in tumours via the temporal integration of the imaging signals triggered by tumour acidosis. This method exploits the catastrophic disassembly, at the acidic pH of the tumour milieu, of pH-sensitive positron-emitting neutral copolymer micelles into polycationic polymers, which are then internalized and retained by the cancer cells. Positron emission tomography imaging of the ⁶⁴Cu-labelled polymers detected small occult tumours (10-20 mm³) in the brain, head, neck and breast of mice at much higher contrast than ¹⁸F-fluorodeoxyglucose, ¹¹C-methionine and pH-insensitive ⁶⁴Cu-labelled nanoparticles. We also show that the pH-sensitive probes reduce false positive detection rates in a mouse model of non-cancerous lipopolysaccharide-induced inflammation. This macromolecular strategy for integrating tumour acidosis should enable improved cancer detection, surveillance and staging.