The Buddha frequently traveled to Griddhkuta and Jivaka amravana and the proximity of Udumbarika Paribbajakarama to these places must have drawn him to this place. These frequent visits offered the Paribbajakas some opportunity to discuss his views and compare with other thoughts prevailing at the time. A few of such conversation with few famous Paribbajaka is recorded in Pali literature.
One such conversation is that between the Buddha and the famous Paribbajaka Sakuladayi. The discussion with sakuladayi is preserved in The Mahā-Sakuladāyī and the Culla Sakuladāyī Suttas. The Buddha during one his visits discusses perfection with Sakuladāyi. The Buddha clarified that Sakuladāyi’s conception of perfection is vague and undefined and with further proofs and examination explains that it’s empty and faulty. In answer to Sakuladāyi's question as to what the Buddha would define as absolute bliss; the Buddha explains the four Jhānas and the destruction of the āsavas.
Sakuladayi then wants to know: 'What are the past and what the future?'
'Let the past be,' answered the Buddha, 'and forget the future. I will teach you that which is now.'
When this condition is, that condition comes to be,
With the arising of this, that arises,
When this is not here, that does not come into existence,
With the ceasing of this, that too ceases.
After the conversation Sakuladayi wanted to enter the Buddhist monkhood but because of the opposition from his followers he could not do so (M.II. 39) (Buddhist Monastic Life by Mohan wijayaratna, P.9) but there is also a reference (M.ii.29ff).of Sakuladāyi eventually converts to Buddhism.
Udumbarika Paribbajakarama used to be a centre of Paribbajaka of various denominations as suggested by the Pali sources and more than 150 recluses were staying at the Paribbajaka arama when Buddha had discourse with Sakuladayi. And few among them were very prominent Paribbajaka who were present on this occasion like Annabhara and Varadhara (A.ii.29, 176, MA. Ii. 716)
Another important discourse that took place here was with Paribbajaka Nigrodha and the discussion is preserved in Udumbarika-Sīhanāda Sutta.
Sandhana, who was a disciple of the Buddha, was on his way to see the Buddha. He stopped at the paribbajakarama because it was early for his interview. When Sandhana reached the park he discovered the one hundred and forty score wandering philosophers, all gossiping and talking of various bits of news, debating theories, and passing around rumors
Sandhana found Paribbajaka Nigrodha, and they greeted each other kindly and took seats.
"I find it interesting”, said Sandhana, how the wanderers in this loose confederation conduct themselves. The manner of conversation and passing along gossips and rumors with the noise it creates is almost a shock, given the sheer number of men present here. He said he likes the Buddha’s rules of conducts in this field much better; reclusive in the forests, silent and away from infuriating things like gossip and rumors.
Nigrodha decided to take this personally, and he countered, rather than replying with logic and wisdom,
"Aye? Tell me now, you white robed layman, who does Gotama talk to and converse with? How can he possibly sharpen his speaking-skills or his mental abilities away from other people?
Nay, I say that Gotama grows weaker in wisdom for his solitude, not stronger. He is not accustomed to crowds, he is not in touch with the people, and he is, no doubt, a poor debater.
Hah! In fact, if he were to come to this Park right now, this very instant, we would befuddle and confuse him with one question; he would topple over like an empty jar."
The Buddha upon hearing about this conversation left his retreat and went down from the Griddhkuta towards the Park with the intention of clearing the misunderstanding. Nigrodha caught site of him approaching and coaxed his men down to silence, as his last statement had brought them to cheering.
He said to them, "Quiet, my men, quiet! We want that Gotama to come to us, and if we appease his desire for a quiet atmosphere, he will no doubt come. If he does come, we’ll ask him what his doctrine is."
Then the Buddha approached Nigrodha and the Buddha took a seat and said,
"Nigrodha, I say to you that this Dhamma is going to be impossible for you to grasp. Why’s this? Because, Nigrodha, you hold onto different beliefs, you have different inclinations, and you are exposed to different experiences. Why don’t we instead talk of something more pleasant for you and your fellows? Let’s talk about your doctrines instead."
Nigrodha, after imploring his fellows to cease their murmuring, stated to the Buddha, "Sire, we preach soberness and strictness, seriousness and rigor. We regard austerities of the highest quality to be vital. As such, however, what do you think, Venerable Gotama, fulfills them?"
In explaination the Buddha asked him a question:
"A decent question in its own right, Nigrodha. Take a man who practices self-torture, going naked and without food and water, abusing himself, behaves like a dog, licking his hand and eating what food he does take raw and uncooked, ignoring the wishes of others. Or, when he needs to wear clothing, he uses rough clothes, the kind dead bodies are wrapped in. He makes his bed with thorn branches and dry hay, and he is dirty and unwashed. Or he washes three times before the sun sets, but he takes no water. Nigrodha, does such a man, in any of those instances, meet your marks for austerities?"
Nigrodha agreed saying that, "Indeed, such man doing any of those practices would."
"I maintain that they are in fault, Nigrodha", said Buddha.
The Buddha turned the discussion on to the merits and demerits of self-mortification and explaining that for the spiritual practice the body has to be treated like a vehicle and not a road block that needs to be punished and diminished; and ended up teaching the purpose of his own school of thoughts. Nigrodha expressed great admiration for the Buddha's exposition, but his ego kept him and his disciples from becoming followers of the Buddha (D.iii.36ff).