By practicing Yoga and pranayama (control of prana vayu) a Yogi can float in the air, walk in air. This is called Vayu-Siddhi or mastery over air. It can be achieved in the third stage of pranayama sadhana.
From Shiva Samhita:
In the first stage of pranayama the body of the Yogi begins to
prespire. When it prespires, he should rub it well, otherwise the body
of the Yogi loses its dhatu (humours).
In the second stage, there takes place the trembling of the body. In
the third, jumping about like a frog; and when the practice becomes
greater, the adepts walk in the air.
When the Yogi, though remaining in Padmasana, can rise in the air and
leave the ground, then know he has gained Vayu-Siddhi (success over
air), which destroys the darkness of the world.
There are many siddhis (perfections) that are obtained by the adept Yogi and among which floating (or walking ) in the air is one.
The Yogi acquires the following powers:- Vakya siddhi (prophecy),
transporting himself everywhere at will (Kamachari), clairvoyance
(duradrishti), clairaudience (durasruti), subtle-sight (sukshma
drishti) and the power of entering another's body (parakayapravesha),
turning base metals into gold them with his excrements and urine and
the power of becoming invisible and lastly, moving in the air.
Also, among the six chakras, the Anahata Chakra is ruled by the Vayu Tattva
. An adept Yogi, by contemplating on this chakra & by mastering it, can
achieve mastery over vayu or air. Then he can walk in air
In the heart, is the 4th chakra, the Anahata. It has twelve
petals....He who always contemplates on this lotus of the heart is
eagerly desired by celestial maidens.....
He gets immeasuarable knowledge, knows the past, present and future
time ; has clairaudience, clairvoyance and can walk in air whenever he
He sees the adepts and the Goddesses known as Yoginis; obtains the
power known as Khechari, and conquers all who move in the air.
He contemplates daily on the Banalinga [which is situated in the
Anahata Chakra] undoubtedly obtains the perfections called Khechari
(moving in air) and Bhuchari (going at will all over the world).
So, a highly adept Yogi can float or walk on air.