The bodies were [and will be] completely spiritual

In truth, before [Adam and Chava] transgressed the command of the Holy One, their bodies were also completely spiritual, like our physical bodies shall be after complete refinement...when comprehension of G-dliness will give life to the body like physical eating and drinking does [at present]. This is what Adam's body was before the sin...that his heel was brighter than the sun.

Ohr Hatorah, Bereishis vol. VII (page 2326 (1163a))

Bodies of the Future (part IV)

Regarding Adam Harishon[...] there was no death, and tehre was no relevance to refinement or purification at all. Like it was by the body of Adam Harishon, so too the bodies in the time of resurrection will be completely holy and pure and will live forever. In fact, the truth is that the bodies that will be in the time of the resurrection will be on a higher level than like the body of Adam Harishon, that although the body of Adam Harishon was holy and pure, yet there was the sin of the tree of knowledge; in the time of the resurrection of the dead there will certainly be no relevance to the subject of sin at all. Because at the Creation the man was in a state of perfection, but the world contained the existence of "shells", only that their place was very low. The intent being that their correction should come about through the labor of the man, because the way of labor is only when there is a source of opposition and temptation and deception; thus, even though the body of Adam Harishon was the formation of the hands of the Holy One, blessed be He, it was in a way which allowed for the possiblity [of choosing evil], for if not then there would be no labor at all. But at the resurrection of the dead, which is after the correction and refinement, because during the days of Moshiach the spirit of evil will be removed, and all the moreso in the time of the resurrection of the dead there will be the bringing into being of the body on a higher level and it will be on the ultimate level of perfection even higher than the body of Adam Harishon.

Sefer Hamaamorim 5711 (Rebbe Rayatz) p.207

Bodies of the Future (Part III)

There will be a final purification of the body, that it will be refined from physicality and from its nature entirely. At the resurrection of the Dead the souls will rise in bodies, that those bodies will also be physical but not from being born from a father and mother, but rather from the dew of resurrection, which means He will cover them with skin and flesh, like the bones that Yechezkiel revived, as is known that from the bones of the body of the present era, there remains only the Luz bone, which is in the back of the neck where the knot of the tefillin goes. The Luz bone will be the beginning of the building of the future body, as it states in Likutei Torah of the Arizal, parshas Bereishis, which means that there won't be a body from a physical mother and father, even though there will be a physical body it will be brought into being by the Holy One, bleseed be He, via the dew of resurrection, Tala d'Atika. And being that the body of the resurrection will be from the Holy One, blessed be He, via the dew of Resurrection, thus tey will be completely holy and pure bodies, like the body of Adam Harishon, who was the formation of G-d's hands, that his body was holy from the Supernal Holiness (kodesh elyon), and his heel made the sun dark, that his body was completely refined and pure like light, and he made the light of the sun appear dark, meaning that his body and soul were similar to each other.

Sefer Hamaamorim 5711 (Rebbe Rayatz) p.207

Bodies of Future (part II)

In the days of Moshiach, even though there will be the ultimate level of refinement, nonetheless there will be physical bodies, and the fulfillment of mitzvos will be in physicality, just that it will be on the ultimate level of perfection, as we say "there we will perform mitzvos like Your will". In the days of Moshiach there will be offerings like the mitzvos of Your will, because it is the man which offers an animal, and at present the aspect of man is not in a state of perfection, but in the days of Moshiach the aspect of man will indeed be in a state of perfection and evil will have been removed and there will only by the aspect of the image of G-d (Tzelem Elokim). Specifically at this time will there be the aspect of "mitzvos like Your will." Then, all the mitzvos will be in the ultimate perfection, but nonetheless they will be mitzvos of physical action and it will all be in physicality, as it says "there is no difference between this world and the days of Moshiach besides servitude to the nations," because the spirit of impurity will be removed from the earth, and materiality will be purified.

Sefer Hamaamorim 5711 (Rebbe Rayatz) p.207

Bodies of the future (Part I)

It is known that the Resurection of the Dead will be after the days of Moshiach[...] Now, in the days of Moshiach the bodies will be completely refined, as it says "I will remove the spirit of impurity from the land," and as a consequence of the removal of the impurity, all the materiality and physicality will be refined, until even among animals and beasts the pollution will cease. This is as it states "the wolf will dwell with the lamb and the cow and bear, etc"

Specifically it the bodies of human beings that will be the most refined, but nonetheless there will be bodies which will be born from a physical mother and father from a natural physical desire. This desire, however, will not be a material desire at all, and there will be no admixture of evil in it, as it says in the Zohar "the tree of knowledge of good and evil will be removed from the world" (Zohar III 124b). Nevertheless, there will be a natural desire, and this is like Adam Harishon before the sin, that he didn't have material desires at all, just the "will", like the "will" to eat, not for fulfilling his desires but rather for the connection of the soul and body that comes about from the eating. And so, too, the union of man and woman was out of the desire to bring children.

Sefer Hamaamorim 5711 (Rebbe Rayatz) p.20

Resurrection: An Intermediary Stage

The elevations of the souls from the lower Gan Eden to the higher Gan Eden is via the [intermediary of] Nahar Dinur (river of fire) which is the pillar in Gan Eden which includes the concept of self nullification (bitul), [that one must have bitul] in order to come from the lower Gan Eden to the higher.

So, too, in the days of Moshiach there will be a resurrection of the dead as an intermediary level until the World to Come in the 7th millenium. The difference between immersing in the Nahar Dinur or becoming nullified in the pillar [on the one hand] and the level of intermediary in the days of Moshiach which refers to the resurrection of the dead, is that the immersion in the Nahar Dinur is nullification for the soul alone and not the physical bodies. But the resurrection that is after the days of Moshiach is the aspect of nullification for the bodies as well, meaning that the physical bodies themselves will grasp the Divine light and they will be on the level of self-nullification of their very existence.

Maamorim of the Alter Rebbe, 5565, I:412

G-dly Bodies

Those born from Adam and Chava before the sin were on the level of pure and holy bodies of an aspect of G-dliness, this is really a man of G-d, etc., He really made a tzelem Elokim, and Kayin and Hevel (Cain and Abel). So it will really be in the time to come at the resurrection of the dead...the same body...that body will possess the ultimate level of disrobing from physicality. The situation of no eating or drinking is right after the resurrection of the dead.

Maamorim Mitteler Rebbe, Vayikra II p. 686

Refining the Body to Surpass Adam Harishon

As our sages say, there is no difference between this world and the days of Moshiach except servitude to the nations. The service will only be in a spiritual manner, and not like Adam Harishon in Gan Eden to work it, etc. in spirituality itself, but rather [it will be] in real physicality itself...but still there will be death because we didn't yet refine the body to the level of Adam before the sin. But at the revival of the dead, when all the souls which passed away will come and go up higher and higher to their bodies...and the bodies will be pure and holy.

Maamorim Mitteler Rebbe, Vayikra II p. 686