ABSTRACT Latin American migration to Australia spans over five decades. Despite growing Latin American diasporas in Australia, little is known in public imaginaries about the difficult histories, desires and struggles that have shaped those who fled their countries due to conflict and dictatorships. This article draws from fifteen in-depth interviews with Spanish-speaking migrants from post-conflict and dictatorial Latin America living in Australia. Engaging with decolonial knowledge and scholarship in Latin American memory studies, the article argues for desire-centred memory work in which trauma, damage and deficit narratives are decentred. Through theorising with ambiguity and participants’ voices, I reveal the potential of taking seriously everyday memories of joy, care, and desire to unsettle and nuance normative understandings of difficult histories, including Latin American migration to Australia. In doing so, I also emphasise the importance of engaging with people as epistemic subjects who are doing the difficult memory work by choosing how, when, and where to narrate and share their stories. Ultimately, this article contributes to decolonial, feminist and Southern epistemologies and understandings of memory in the wake of violence that are desire-based (Tuck, E., 2009. Suspending Damage: A Letter to Communities. Harvard Educational Review, 79 (3), 409–427) and transformative.