Conditional address translation is performed in a multi-tenant cloud infrastructure to effectively support tenant-assigned addresses. For each tenant, the multi-tenant cloud infrastructure deploys both a private network used to communicate between the tenant and the cloud and a tenant-facing gateway to manage the private network. The multi-tenant cloud infrastructure also includes an externally-facing gateway used to communicate between the multi-tenant cloud and a public network. The tenant-facing gateways are configured to bypass address translation—providing consistent addressing across each private network irrespective of the physical location of resources linked by the private network. By contrast, the public-facing gateway is configured to translate source addresses in outgoing packets to addresses that are unique within the public network. Advantageously, discriminately mapping addresses enables multiple tenants to interact in a uniform fashion with both on-premises resources and cloud-hosted resources without incurring undesirable address collisions between tenants.