Pleased with the king he had sent below, Vishnu offers Bali a wish; Bali asks for three days of his own on earth each year and for Lakshmi to stay in every house that lights lamps for him. The Padma Purana gives the same festival as Shiva's answer to Kartikeya.
Having taken the earth from Bali as the dwarf, Hari is pleased with him and offers a boon.
Bali asks for three days of rule on earth each year, for Lakshmi to stay in houses that light lamps, and for the darkness of her shadow to fall on dark houses.
On the new-moon day the gods and Lakshmi are freed from Bali's prison and sleep in the Milk Ocean; Lakshmi sleeps in a lotus.
The demons find Lakshmi asleep and praise her as the goddess in the flame of the lamp.
Women wake Lakshmi before Hari wakes; the king declares the kingdom of Bali and walks the city at midnight.
After midnight the women drive Alakshmi out of the courtyards with winnowing baskets and drums.
In the Padma Purana Kartikeya asks Shiva why Diwali is kept, and Shiva tells of the Yama lamp, the oil bath, the lamps, the game of dice he lost to Gauri, Govardhan worship and the worship of Bali painted in five colours.
Hari, pleased with Bali after taking the earth from him as the dwarf, offers a boon. Bali asks that Lakshmi stay permanently in the houses of those who light lamps in his kingdom on earth, that the darkness of Lakshmi's shadow fall on houses left dark, and that his reign last for three days, the fourteenth, the new moon and the first of Karttika. On the new moon the gods and Lakshmi were set free from Bali's prison and went to sleep in the Milk Ocean, Lakshmi within the lotus; so beds are made for her and she is woken by women before Hari wakes. The demons, afraid of Vishnu, came and praised the sleeping Lakshmi as the splendour of sun, moon, fire, lightning, gold and stars, stationed in the flame of the lamp. The king decorates the city, feeds the hungry, announces 'today is the kingdom of Bali', gives children toys and walks the city at midnight. After midnight the women of the city drive Alakshmi out of their courtyards with winnowing baskets and small drums.
Kartikeya asks Shiva what the fruit of Dipavali is, why it is kept and which god presides. Shiva prescribes the Yama lamp outside on the thirteenth, the oil bath on the fourteenth (Lakshmi in the oil, Ganga in the water), lamps in temples, at rivers, gateways, cowsheds and elephant stalls, and the waking of Lakshmi by women before Hari wakes. He tells how he and Bhavani sat down to dice while Lakshmi stood by as a cow, and how Gauri beat him and sent him away naked, so that Shankara is unhappy and Gauri always happy. After midnight Alakshmi is driven out with drums; in the morning Govardhan is worshipped and cows are adorned and neither milked nor loaded; at night Bali is painted in five colours with the Vindhya range and worshipped as 'son of Virochana, future Indra'. Vishnu granted Bali this festival, the Kaumudi, named from 'ku', the earth, and 'mud', delight.
What is different here:
Told by Shiva to Kartikeya as instructions; adds the game of dice that Shiva lost to Parvati and the painted image of Bali; leaves out Bali's own request.
Sources: The Skanda Purana, tr. G. V. Tagare (Motilal Banarsidass), Vaishnava Khanda, Karttikamasa Mahatmya, chapter 9: Rites on Vatsadvadashi, Yamatrayodashi, Narakachaturdashi and Dipavali, on Wisdom Library; Padma Purana, Uttara Khanda, adhyaya 122 (Dipavali), Sanskrit with English rendering, VedaPath