Cortical circuits contain multiple types of inhibitory neurons which shape how information is processed within neuronal networks. Here, we asked whether somatostatin-expressing (SST) and vasoactive intestinal peptide-expressing (VIP) inhibitory neurons have distinct effects on population neuronal responses to noise bursts of varying intensities. We optogenetically stimulated SST or VIP neurons while simultaneously measuring the calcium responses of populations of hundreds of neurons in the auditory cortex of male and female awake, head-fixed mice to sounds. Upon SST neuronal activation, noise bursts representations became more discrete for different intensity levels, relying on cell identity rather than strength. By contrast, upon VIP neuronal activation, noise bursts of different intensity level activated overlapping neuronal populations, albeit at different response strengths. At the single-cell level, SST and VIP neuronal activation differentially modulated the response-level curves of monotonic and nonmonotonic neurons. SST neuronal activation effects were consistent with a shift of the neuronal population responses toward a more localist code with different cells responding to sounds of different intensity. By contrast, VIP neuronal activation shifted responses towards a more distributed code, in which sounds of different intensity level are encoded in the relative response of similar populations of cells. These results delineate how distinct inhibitory neurons in the auditory cortex dynamically control cortical population codes. Different inhibitory neuronal populations may be recruited under different behavioral demands, depending on whether categorical or invariant representations are advantageous for the task.