Step 1: Describe the radiographic texture. Countless small, uniform, well-distributed nodules in the millimetre range filling both lungs like sprinkled seeds is the classic miliary pattern, pointing directly to miliary tuberculosis.
Step 2: Connect pattern to mechanism. Such even, bilateral micronodular spread arises when Mycobacterium tuberculosis disseminates through the bloodstream and seeds the lungs diffusely, which is why the nodules are so regular and widespread.
Step 3: Contrast with the alternatives. Bronchiectasis gives dilated bronchi and ring or tram-track shadows, COPD gives over-inflated lucent lungs with low flat diaphragms, and lung cancer gives a focal mass rather than diffuse tiny seeds, so none reproduce the millet-seed look.
Step 4: Confirm. The combination of micronodules of 1 to 5 mm and uniform distribution is specific enough that the depicted condition is miliary TB.
\[\boxed{\text{Miliary tuberculosis}}\]