BackgroundSubstance use disorders (SUDs) commonly co-occur with one another and with other psychiatric disorders. They share common features including high impulsivity, negative affect, and lower executive function. We estimate the shared genetic architecture across distinct SUDs, its independence from genetic liability to substance use, and its relation to genetic liability to impulsivity, negative affect, and executive function as well as non-substance psychopathology.MethodsWe tested whether a common genetic factor undergirds liability to problematic alcohol use (PAU), problematic tobacco use (PTU), cannabis use disorder (CUD), and opioid use disorder (OUD) by applying Genomic structural equation modelling to genome-wide association study statistics (Total N = 1,019,521; substance specific Ns range: 82,707-435,563 of European ancestry), while adjusting for the genetics of substance use (Ns = 184,765-632,802). We tested whether shared liability across SUDs is associated with behavioral constructs (risk taking, executive function, neuroticism; Ns = 328,339-427,037) and non-substance use psychopathology (mood/psychotic, compulsive, and early neurodevelopmental disorders).ResultsShared genetic liability to PAU, PTU, CUD, and OUD was characterized by a unidimensional addiction factor (termed a(g)), independent of substance use. OUD and CUD demonstrated the largest loadings. a(g) was associated with risk taking, neuroticism, executive function, and non-substance psychopathology, but retained specific variance (standardized residual= .579).InterpretationA common genetic addictions factor partly explains susceptibility for alcohol, tobacco, cannabis and opioid use disorder. a(g) has unique pathways that are not shared with substance use or non-substance psychopathology, suggesting that addiction is not the linear combination of substance use and psychopathology.