This trial consists of 2 parts, i.e., Part Ia and Ib. The Part Ia is to evaluate the safety and tolerability of a single intravenous dose of af-001 in patients with radically unresectable, recurrent, metastatic differentiated thyroid cancer (papillary carcinoma, follicular carcinoma) refractory to or intolerant of standard-of-care therapy, who have received total thyroidectomy, and to determine the MTD (Maximum tolerated dose).

Part Ib is to evaluate the efficacy and safety of af-001 mutiple doses to patients with radically unresectable, recurrent, metastatic differentiated thyroid cancer (papillary carcinoma, follicular carcinoma), who have received total thyroidectomy and are RAI naïve, randomized into two arms at the determined MTD or the MTD-1 dose level, and to determine the recommended Phase II dose (RP2D)

The Part Ia is a dose escalation part. The Part Ib is a parallel-group comparative study part based on the MTD determined in Part Ia, in which 10 patients each will be randomly assigned to one of two treatment arms, at the MTD for af-001 or the MTD-1 dose level. Patients will be randomly assigned by the enrollment system (allocated at a ratio of 1:1). Random assignment will be performed using the stratified permuted block method. The stratification factor will be the site(s) of metastases.

Inclusion Criteria:

<Ia part>

• Patients with differentiated thyroid cancer (papillary carcinoma, follicular carcinoma) after total thyroidectomy.
• Patients with radically unresectable, recurrent, metastatic disease who are judged by the principal investigator or sub-investigator (hereinafter, "principal/sub-investigators") to be refractory to or intolerant of standard-of-care therapy.

<Ib part>

• Patients with radically unresectable, recurrent, metastatic disease who are RAI naive
• Patients with measurable lesions. <Ia/Ib part>
• Patients with an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 to 2 and stable general condition.
• Patients expected to survive for at least 6 additional months based on clinical symptoms and physical examination findings.

Exclusion Criteria:

<Ia/Ib part>

• Patients who need to preserve fertility.
• Females who are pregnant or may be pregnant, breastfeeding patients, or patients or their partners who cannot agree to appropriate contraception.
• Patients with active multiple cancers (synchronous multiple cancers and ectopic double cancers with a disease-free period of <=3 years).
• Patients with uncontrolled active infections.
• Patients who are positive for hepatitis B virus surface (HBs) antigen, hepatitis C virus (HCV) antibodies, or human immunodeficiency virus (HIV) antibodies.