Stroke or Transient Ischemic Attack (TIA): Given the recent coronary angioplasty, there's an increased risk of cerebral embolism leading to stroke or TIA, which can cause diplopia due to involvement of the brainstem or cranial nerves controlling eye movements.

Coronary Angioplasty-related Complications: Complications from the procedure itself, such as vasovagal reaction or direct injury to nerves, could potentially lead to transient diplopia.
Medication Side Effects: Certain medications used during or after the procedure (e.g., anticoagulants, sedatives) might have side effects that include diplopia.
Hypertension or Hypotension: Blood pressure fluctuations post-procedure could lead to cerebral or ocular complications causing diplopia.

Subarachnoid Hemorrhage: Although less likely, a subarachnoid hemorrhage could occur due to the procedure or underlying conditions and must be ruled out due to its high mortality rate.
Cavernous Sinus Thrombosis: A rare but potentially life-threatening condition that could arise from facial or sinus infections, which might not be directly related to the angioplasty but could be missed in the differential diagnosis.
Wernicke's Encephalopathy: Especially if the patient has a history of alcohol abuse, this condition can cause ophthalmoplegia and should not be overlooked.

Multiple Sclerosis: An initial presentation or exacerbation of multiple sclerosis could theoretically cause diplopia, although it would be an uncommon coincidence post-angioplasty.
Myasthenia Gravis: A rare autoimmune disorder that could cause fluctuating muscle weakness, including eye muscles, leading to diplopia.
Thyroid Ophthalmopathy: If the patient has a history of thyroid disease, thyroid ophthalmopathy could potentially cause diplopia, although it's less directly related to the recent procedure.