Step 1: The diagnosis is acute respiratory distress syndrome (ARDS). It is a form of respiratory failure caused by rapid, widespread inflammatory injury to the lungs.
Step 2: Acute pancreatitis is a classic non-pulmonary trigger of ARDS. Systemic inflammatory mediators damage the alveolar-capillary membrane, causing non-cardiogenic pulmonary oedema that presents on day 3-7 with breathlessness and bilateral basal crepitations.
Step 3: The chest radiograph shows bilateral opacities not fully explained by effusion, lobar or whole-lung collapse, or a nodule - meeting the Berlin imaging criterion for ARDS. Why the distractors are wrong: bilateral pneumonia would usually be infective with a different clinical course; pulmonary embolism does not give diffuse bilateral alveolar opacities; and collapse produces volume loss and mediastinal shift, not diffuse infiltrates.