According to SN 7.21 (quoted below), one could purify oneself of sins, not by water purification (as practised by Brahmins), but rather by dipping oneself in the lake of the Dhamma (Buddha's teachings) which has the shore of virtues (sila) - in order words, by practising the teachings, we can purify ourselves.
The Buddha said to Sangarava:
“Is it really true, brahmin, that you practice purification by water,
believing in purification by water; that you live committed to the
practice of immersing yourself in water at dawn and dusk?”
“Yes, Master Gotama.”
“But brahmin, for what reason do you practice purification by water?”
“It’s because, Master Gotama, whatever bad deeds I’ve done during the
day I wash off by bathing at dusk; and whatever bad deeds I’ve done
during the night, I wash off by bathing at dawn. That’s the reason why
I practice purification by water.”
“The teaching is a lake with shores of ethics, brahmin,
unclouded, praised by the fine to the good.
There the knowledge-masters go to bathe,
and cross to the far shore without getting wet.”
When he had spoken, Saṅgārava said to the Buddha:
“Excellent, Master Gotama! Excellent! … From this day forth, may
Master Gotama remember me as a lay follower who has gone for refuge
for life.”
According to the Salt Crystal Sutta (quoted below), the notion of purification by practising the teachings is expounded further, through the explanation that one should be "developed in [contemplating] the body, developed in virtue, developed in mind, developed in discernment: unrestricted, large-hearted, dwelling with the immeasurable". If you dive deep into what this phrase means, that's all you need to cleanse your negative past completely. You can find some useful commentary by Piya Tan here.
"Suppose that a man were to drop a salt crystal into a small amount of
water in a cup. What do you think? Would the water in the cup become
salty because of the salt crystal, and unfit to drink?"
"Yes, lord. Why is that? There being only a small amount of water in
the cup, it would become salty because of the salt crystal, and unfit
to drink."
"Now suppose that a man were to drop a salt crystal into the River
Ganges. What do you think? Would the water in the River Ganges become
salty because of the salt crystal, and unfit to drink?"
"No, lord. Why is that? There being a great mass of water in the River
Ganges, it would not become salty because of the salt crystal or unfit
to drink."
"In the same way, there is the case where a trifling evil deed done by
one individual [the first] takes him to hell; and there is the case
where the very same sort of trifling deed done by the other individual
is experienced in the here & now, and for the most part barely appears
for a moment.
'Now, a trifling evil act done by what sort of individual takes him to
hell? There is the case where a certain individual is undeveloped in
the body, undeveloped in virtue, undeveloped in mind [i.e.,
painful feelings can invade the mind and stay there], undeveloped in
discernment: restricted, small-hearted, dwelling with suffering. A
trifling evil act done by this sort of individual takes him to hell.
'Now, a trifling evil act done by what sort of individual is
experienced in the here & now, and for the most part barely appears
for a moment? There is the case where a certain individual is
developed in the body, developed in virtue, developed in mind
[i.e., painful feelings cannot invade the mind and stay there],
developed in discernment: unrestricted, large-hearted, dwelling with
the immeasurable. A trifling evil act done by this sort of individual
is experienced in the here & now, and for the most part barely appears
for a moment.
The teachings on the Brahmaviharas in particular are further elaborated in AN 10.219.