Actualizar la columna en la tabla de Facturas con el total de pago de la tabla de Pagos.

Tengo 2 tablas (mostradas a continuación) – Invoice y Payments. Una sola factura puede tener múltiples pagos. Necesito SUMAR el total de PayAmt de Payments y actualizar la columna PayTotal en la tabla Invoice.

Esto NO está funcionando:

UPDATE Invoices
SET Invoices.PayTotal = Payments.Total
FROM Invoices
INNER JOIN
(SELECT InvNum_FK, SUM(PayAmt) as Total
FROM Payments) ON Invoices.InvNum_PK = Payments.InvNum_FK

CREATE TABLE dbo.Invoices
(
    InvNum_PK nvarchar(255) PRIMARY KEY,
    InvAmt    money,
    InvDate   date,
    CustName  nvarchar(255),
    PayTotal  money,
    PayCount  int
);

CREATE TABLE dbo.Payments
(
    PayNumPK int PRIMARY KEY,
    InvNumFK nvarchar(255) 
        FOREIGN KEY REFERENCES dbo.Invoices(InvNum_PK),
    PayAmt    money,
    PayDate   date,
);

INSERT INTO Invoices 
VALUES ('GLI101', 838.93, '2021-08-01', 'George Washington', 0, 0);
INSERT INTO Invoices 
VALUES ('GLI202', 1280.26, '2021-08-02', 'Abe Lincoln', 0, 0);
INSERT INTO Invoices 
VALUES ('GLI303', 1456.23, '2021-08-03', 'Tom Jefferson', 0, 0);
INSERT INTO Invoices 
VALUES ('GLI404', 1124.97, '2021-08-04', 'Jim Madison', 0, 0);

INSERT INTO Payments VALUES (1, 'GLI101', 223.33, '08/15/2021')
INSERT INTO Payments VALUES (2, 'GLI101', 211.88, '09/16/2021')
INSERT INTO Payments VALUES (3, 'GLI101', 316.44, '09/14/2021')
INSERT INTO Payments VALUES (4, 'GLI404', 415.46, '09/10/2021')
INSERT INTO Payments VALUES (5, 'GLI404', 115.46, '09/04/2021')