What did the early church fathers (pre-5th c.) teach with regards to baptismal regeneration? The title says it all, really. 

What did the ECF believe and teach with regards to baptismal regeneration?

Did they generally subscribe to it or deny it? 

Related: What did the early church fathers (pre-5th c.) teach with regards to the doctrine of baptism as a necessity for salvation?
Justin Martyr wrote a chapter (LXI) on Christian baptism in his First Apology, written sometime in the 2nd century:


  I will also relate the manner in which we dedicated ourselves to God
  when we had been made new through Christ; lest, if we omit this, we
  seem to be unfair in the explanation we are making. As many as are
  persuaded and believe that what we teach and say is true, and
  undertake to be able to live accordingly, are instructed to pray and
  to entreat God with fasting, for the remission of their sins that are
  past, we praying and fasting with them. Then they are brought by us
  where there is water, and are regenerated in the same manner in which
  we were ourselves regenerated. For, in the name of God, the Father and
  Lord of the universe, and of our Saviour Jesus Christ, and of the Holy
  Spirit, they then receive the washing with water. For Christ also
  said, Except ye be born again, ye shall not enter into the kingdom of
  heaven [John 3:5].  Now, that it is impossible for those who have
  once been born to enter into their mothers’ wombs, is manifest to all.
  And how those who have sinned and repent shall escape their sins, is
  declared by Isaiah the prophet, as I wrote above, he thus speaks:
  Wash you, make you clean; put away the evil of your doings from your souls; learn to do well; judge the fatherless, and plead for the
  widow: and come and let us reason together, saith the Lord. And though
  your sins be as scarlet, I will make them white like wool; and though
  they be as crimson, I will make them white as snow. But if ye refuse
  and rebel, the sword shall devour you: for the mouth of the Lord hath
  spoken it [Isaiah 1:16-20].  And for this [rite] we have
  learned from the apostles this reason. Since at our birth we were born
  without our own knowledge or choice, by our parents coming together,
  and were brought up in bad habits and wicked training; in order that
  we may not remain the children of necessity and of ignorance, but may
  become the children of choice and knowledge, and may obtain in the
  water the remission of sins formerly committed, there is pronounced
  over him who chooses to be born again, and has repented of his sins,
  the name of God the Father and Lord of the universe; he who leads to
  the laver the person that is to be washed calling him by this name
  alone. For no one can utter the name of the ineffable God; and if any
  one dare to say that there is a name, he raves with a hopeless
  madness. And this washing is called illumination, because they who
  learn these things are illuminated in their understandings. And in the
  name of Jesus Christ, who was crucified under Pontius Pilate, and in
  the name of the Holy Ghost, who through the prophets foretold all
  things about Jesus, he who is illuminated is washed.


Cyprian of Carthage, another Ante-Nicene Father, wrote in the 3rd century of his own baptism:


  For as I myself was held in bonds by the innumerable errors of my
  previous life, from which I did not believe that I could by
  possibility be delivered, so I was disposed to acquiesce in my
  clinging vices; and because I despaired of better things, I used to
  indulge my sins as if they were actually parts of me, and indigenous
  to me. But after that, by the help of the water of new birth [i.e.,
  baptism], the stain of former years had been washed away, and a light
  from above, serene and pure, had been infused into my reconciled
  heart,—after that, by the agency of the Spirit breathed from heaven, a
  second birth had restored me to a new man;—then, in a wondrous manner,
  doubtful things at once began to assure themselves to me, hidden
  things to be revealed, dark things to be enlightened, what before had
  seemed difficult began to suggest a means of accomplishment, what had
  been thought impossible, to be capable of being achieved; so that I
  was enabled to acknowledge that what previously, being born of the
  flesh, had been living in the practice of sins, was of the earth
  earthly, but had now begun to be of God, and was animated by the
  Spirit of holiness (Epistle I, To Donatus).


These are the earliest sources I could find who comment on the nature of baptism.  I am sure there are many, many such commentaries among the Post-Nicene Fathers, but rather than search through them I thought I would simply quote what John of Damascus wrote later in his An Exact Exposition of the Orthodox Faith.  Written in the early 8th century, Exposition was probably the first summary of Church dogmatic theology and reflects the collected teaching of recognized Church Fathers up to that point.  In "Concerning Faith and Baptism", he writes:


  We confess one baptism for the remission of sins and for life eternal.
  For baptism declares the Lord’s death. We are indeed buried with the
  Lord through baptism [Col 2:12], as saith the divine Apostle. So
  then, as our Lord died once for all, we also must be baptized once for
  all, and baptized according to the Word of the Lord, In the Name of
  the Father, and of the Son, and of the Holy Spirit [Matt 28:19],
  being taught the confession in Father, Son, and Holy Spirit.  
  The baptism then into Christ means that believers are baptized into
  Him. We could not believe in Christ if we were not taught confession
  in Father, Son, and Holy Spirit4. For Christ is the Son of the Living
  God5, Whom the Father anointed with the Holy Spirit: in the words of
  the divine David, Therefore God, thy God, hath anointed thee with the
  oil of gladness above thy fellows [Ps 44:7 LXX]. And Isaiah also
  speaking in the person of the Lord says, The Spirit of the Lord is
  upon me because He hath anointed me [61:1]. Christ, however, taught
  His own disciples the invocation and said, Baptizing them in the Name
  of the Father, and of the Son, and of the Holy Spirit. For since
  Christ made us for incorruption, and we transgressed His saving
  command. He condemned us to the corruption of death in order that that
  which is evil should not be immortal, and when in His compassion He
  stooped to His servants and became like us, He redeemed us from
  corruption through His own passion. He caused the fountain of
  remission to well forth for us out of His holy and immaculate side [Jn
  19:34], water for our regeneration, and the washing away of sin and
  corruption; and blood to drink as the hostage of life eternal. And He
  laid on us the command to be born again of water and of the Spirit [Jn
  3:5], through prayer and invocation, the Holy Spirit drawing nigh unto
  the water. For since man’s nature is twofold, consisting of soul and
  body, He bestowed on us a twofold purification, of water and of the
  Spirit: the Spirit renewing that part in us which is after His image
  and likeness, and the water by the grace of the Spirit cleansing the
  body from sin and delivering it from corruption, the water indeed
  expressing the image of death, but the Spirit affording the earnest of
  life.  For from the beginning the Spirit of God moved upon
  the face of the waters [Gn 1:2], and anew the Scripture witnesseth
  that water has the power of purification [Lev 15:10]. In the time of
  Noah God washed away the sin of the world by water [Gn 16:17]. By
  water every impure person is purified, according to the law, even the
  very garments being washed with water. Elijah shewed forth the grace
  of the Spirit mingled with the water when he burned the holocaust by
  pouring on water [3 Kingdoms 18:32 LXX]. And almost everything is
  purified by water according to the law: for the things of sight are
  symbols of the things of thought. The regeneration, however, takes
  place in the spirit: for faith has the power of making us sons (of
  God), creatures as we are, by the Spirit, and of leading us into our
  original blessedness.  The remission of sins, therefore, is
  granted alike to all through baptism: but the grace of the Spirit is
  proportional to the faith and previous purification. Now, indeed, we
  receive the firstfruits of the Holy Spirit through baptism, and the
  second birth is for us the beginning and seal and security and
  illumination of another life