This poster introduces the Innovation Labs framework within the HAICu project, which connects AI and digital humanities researchers with cultural heritage institutions and societal stakeholders. The Labs begin from heritage-sector challenges rather than technological possibilities, embedding researchers in heritage environments to support interdisciplinary collaboration and sustainable research uptake. They provide structured co-creation spaces, integrate advanced AI with contextual knowledge of collections and user constraints, and enable iterative development using rich multimodal data and diverse user communities. Four thematic labs anchor the framework: ‘Deep Journalism Lab’, ‘Histories of Ordinary People Lab’, ‘Citizen Science for Natural History Lab’, and ‘Limitations of AI Lab’. Through collaborative activities and prototype testing, the Labs promote reliable, explainable, user-centred AI tools for heritage and society.