This study investigated the role of generative artificial intelligence (AI) tools in facilitating informal digital English learning activities among second language (L2) learners in a Chinese context. It explored how factors like learners' ideal L2 self-imagination, international posture, and perceptions of information quality influence their engagement with productive (e.g., writing, speaking) and receptive (e.g., reading, listening) informal digital learning activities mediated by generative AI. Drawing from theories of consumption values and self-determination, the research model examined relationships between these variables. The findings suggest that while generative AI holds promise for informal digital language learning by facilitating imagination of an ideal multilingual self, there are opportunities to enhance functionality for L2 contexts. Nurturing an international mindset through interventions may also promote informal learning across genders. Adapting informal digital learning resources based on factors like information quality perceptions could increase engagement. This study provides insights into harnessing generative AI effectively for blended language learning solutions.