The unborn Lord takes birth by his own power, never under compulsion.

Advaita Vedānta

The Lord's birth is not real at all; it is mere appearance produced by maya, for the sake of grace, not in the way things truly stand. Maya here is the power made of the three qualities, the very power under whose sway the whole world turns and by which the world fails to know its own Self. The Lord takes his stand on this nature, brings it under his control, and so comes to be 'as though' possessed of a body, 'as though' born, not in reality as the world is born. The Self in itself is the bodiless mass of being, consciousness, and bliss; the appearance of being human is sheer maya. A juggler, never leaving his own nature and using no real materials, conjures a second juggler climbing a rope in the sky; just so the Lord, remaining the one firm consciousness, by his maya throws up a consciousness-formed body and shows its childhood and youth. The one difference from the juggler is that the Lord never dissolves his maya, so this form is not withdrawn. One strand of this school treats maya as the Lord's eternal causal limiting-adjunct that he masters by the reflection of consciousness and calls his 'body'; another denies any distinction of body and embodied one in the supreme Self at all, holding that the Lord simply rests in his own one-taste form of being-consciousness-bliss and merely behaves as if embodied, the body-hood being mere appearance.

Śaṅkarācārya · Śrī Ānandagiri · Madhusūdana Sarasvatī · Śrī Nīlakaṇṭha · Dhanapati Sūri

Viśiṣṭādvaita

There is no illusion here at all. The Lord gives up not the slightest part of his nature as Lord (his unbornness, his imperishability, his lordship, his mass of auspicious qualities and freedom from all flaw), and presiding over his own essential nature he is genuinely born, by his own will, in a real divine form. Here 'prakriti' does not mean the three-stranded material nature, for the bodies of the descents are not its product; it means his own essential nature ('svabhava'). And the word 'maya' is decisively read as a synonym for knowledge: scripture and the lexicons gloss 'maya' as insight, as wisdom, as in the usage 'by maya he ever knows the good and ill of creatures.' So 'by my own maya' means by my own knowledge, by my own resolve. His form is the luminous divine body the revealed texts describe: sun-colored, beyond darkness, the golden Person within the sun, of true resolve. He simply makes this divine form take a place of the same kind as the bodies of gods and men, by his own resolve, as scripture says, 'unborn, he is born in many ways.'

Rāmānujācārya · Vedānta Deśika

Dvaita

Both the Lord's self and the Lord's body are imperishable; 'of imperishable nature' covers the body too, which is shown to be a special, eternal form (endless, facing every way; the imperishable seed and treasure-house of all the descents). His birth is no modification: governing his own prakriti he is merely perceived as if born, never actually undergoing the suffering or change that real birth would bring. This school carefully distinguishes two roles of prakriti. By the creative prakriti, the cause of all creation, the Lord fashions the bodies of beings such as Vasudeva and the rest; by the deluding power named Durga he is perceived, though unborn, as if born, by those of deluded mind. And 'by his own maya' means by his own knowledge, since prakriti has already been named separately and the lexicon lists awareness, thought, will, and insight among the meanings of 'maya'; reading it again as prakriti would be redundant. The word 'Ishvara' is read in its highest, primary sense: higher even than the rulers Brahma, Rudra, and the rest, the name belongs to him alone.

Madhvācārya · Śrī Jayatīrtha

Śuddhādvaita

The Lord's birth is the doctrinal pivot, and it is neither a fall nor an illusion nor any concession to the world's cycle. It is the becoming-manifest ('avirbhava') of his ever-full, never-divided body of being, consciousness, and bliss, taken up by his own grace to gather his own people to himself. Presiding over his own prakriti, meaning his own uncommon essential form of pure being-consciousness-bliss, the eternal ground of the powers of knowledge and action and the seat of the six majesties, and never letting it go, he makes himself manifest. The reflexive form of the verb wards off any suspicion of an alien cause. The ordinary soul, by contrast, after leaving its own ground and fixing thought on what is other, has its bliss and its lordly qualities hidden and so rolls through birth and death; what looks like the Lord's birth is only that hiding being spoken of, so that his lordly play has its proper object. For the Lord himself, what is called birth is purely manifestation; the body is no encumbrance but a vessel made for play ('lila'), and the teaching that issues from it is devotion saturated with rasa.

Vallabhācārya · Śrī Puruṣottama

Bhakti

The Lord descends ('avatara') of his own will, taking up his own nature, and his form is real and eternal, not a trick. One voice stresses that the Lord, empty of the subtle body of sixteen parts through which an ordinary soul enters a womb, takes his stand on his own prakriti of pure goodness ('shuddha-sattva') and descends in an image of intensified pure-sattva, by his own will, never dragged in by unseen karmic force. Another reads 'prakriti' here as the Lord's own essential form alone (being, consciousness, bliss), expressly excluding the external maya-power, since if prakriti meant maya he would simply become the world through it and nothing special would be conveyed; his birth is for revealing in the world his special eternal forms. This same voice gives a striking reading of 'by my own maya': maya here is the operation of the power of consciousness that veils and reveals the Lord's own forms, so that he hides his earlier-descended forms and unveils the present one, which is why all his forms are not seen at once. The Marathi voice keeps the image of one thing made to look like two in a mirror: the reflected double is no real second thing; the Lord stays the supreme formless Being yet, resorting to maya, appears invested with bodily form for a special purpose. A divine sign is noted across these voices: in the very birth-chamber he was seen with divine weapons, ornaments, and the six majesties.

Śrīdhara Svāmī · Śrīla Viśvanātha · Śrīla Baladeva · Sant Jñāneśvar

Modern

Read against the human condition: man is bound by karma and so is born; he is in the clutches of nature, deluded by its three qualities. The Lord is the exact reverse: he has maya under his perfect control, rules over nature, and so is never in the thraldom of the qualities. He appears born and embodied through his own maya, but is not so in reality, and this apparent embodiment cannot affect his true divine nature in the least. One voice fuses Samkhya with Vedanta: where Samkhya says nature creates the world on its own, the Vedantins hold prakriti to be a form of the supreme Lord, and the world to arise from the Lord governing his own prakriti; this unimaginable power to create the cosmos from his imperceptible form is what the Gita calls maya, with scripture confirming, 'Prakriti is nothing but maya, and the supreme is the Lord of that maya.' A third voice counts exactly six things packed into the verse (three about the Lord: unborn, imperishable, Lord of all; two about his power: prakriti and yogamaya; one about his appearing) and insists that, controlling his prakriti by his yogamaya, he takes his place among us without becoming a soul; the body the eye sees is real, but it is not inert matter built by the laws that make our bodies, it is the very nature of the Lord made visible.

Swami Sivananda · Lokmanya Tilak · Swami Ramsukhdas