Study to Evaluate Long-Term Safety of ASN002 in Subjects With Moderate to Severe Atopic Dermatitis

Inclusion Criteria * Subject with a history of moderate to severe atopic dermatitis who participated in the preceding ASN002AD-201 and ASN002AD-101 study * Subject must be a candidate for prolonged open label ASN002/gusacitinib treatment according to the investigator's judgment. * Subject has been using an emollient daily for at least 1 week prior to Day 1 and agrees to continue using that same emollient daily throughout the study. * Men and women participating in the study must use medically acceptable birth control or total abstinence from sexual intercourse * Subject is willing to participate and is capable of giving informed consent. Note: Consent must be obtained prior to any study-related procedures. * Subjects must be willing to comply with all study procedures and must be available for the duration of the study. * Subject has a body mass index (BMI) ≤ 38 kg/m2. Exclusion Criteria * Subject is a female who is breastfeeding, pregnant, or who is planning to become pregnant during the study. * Subject has clinically infected atopic dermatitis. * A serious uncontrolled condition including hypertension, history of tuberculosis, hepatitis B or C infection, immune deficiency, heart disease, heart conduction disorder, diverticulitis, diabetes, reflux disease requiring protocol pump inhibitor therapy, malabsorption syndrome, or cancer * Subject has a history of skin disease or presence of skin condition that, in the opinion of the investigator, would interfere with the study assessments. * Subject has a history of eczema herpeticum within 12 months, and/or a history of 2 or more episodes of eczema herpeticum in the past. * Willing to comply with discontinuation of certain treatments for AD, as directed by the Investigator.