A 28-year-old woman with known HIV infection (CD4 count 85 cells/μL) presents with acute dyspnea, fever, and cough for 2 weeks. Chest X-ray shows innumerable tiny nodules (1–2 mm) diffusely distributed throughout both lungs in a random pattern, with no cavitation or hilar lymphadenopathy. Sputum smear microscopy is negative. What is the most likely radiological diagnosis?