Progeny of the Celestials
At first, a young Celestial will have children who resemble godblooded of their patrons. The children of a Solar will resemble the godblooded of the Sun, the children of a Lunar will resemble the godblooded of the Moon, and the child of a Sidereal will have the power of the progeny of their caste's Maiden. The same even holds roughly true for Abyssals and Infernals, who produce ghostblooded and demonblooded of their coadjutor respectively.
As an Exalt gains in power and enlightenment, though, their offspring exceed the narrow constraints of humanity. The human form was never meant to contain such terrible force, and the unformed clay of a child who is sired or carried by a Celestial Exalt is warped by the nature of their parent. Unlike the Dragonblooded, they do not have ways that channel such things into the blessing of Exaltation, and in the end, they become… other.
Inhuman. Gods and demons, wrapped in barely mortal flesh.
These progeny are born able to channel essence, they lack the dual-souled nature of mankind and they cannot Exalt. For all their potency, though, such children are not the equals of the Terrestrial Exalted - and when they have more raw power, it is only through monstrous sacrifices and soul-twisting engineering carried out by a doting parent making them into a one-off wonder.
When one of these children are born, they already have their singular soul. No hun or po comes for them - the fantastic power within them has already stirred something to life within their flesh.
Female Exalts find that they produce these strange divine - or monstrous - children more frequently and more easily than male Exalts. Though this may come as a surprise to the mother-to-be, it is a simple consequence of the difference between men and women. A father's contribution to the biological process ends with the conception. The child of a female Exalt spends fifteen months beneath their mother's heart, basking in the radiance of their mother's power.
There are several factors which increase the chance of this happening. The higher the Enlightenment of the parent, the more frequently it occurs. Massive essence exposure increases the chance too - should the mother frequently flare her anima, engage in massive battles or spend long periods in an appropriate demesne, the odds are greatly increased. Deliberate genesis engineering, as some Lunar and Infernal Charms can do can make it a near certainty. On the other hand, things like a reduced gestation period, multiple births or - in the case of a mortal mother - extended separation from the father can reduce the chance drastically.
Most of the progeny below exists in the range of Enlightenment 1 to Enlightenment 5. Akuma can reach Enlightenment 7, but only through deliberate genesis engineering - this is not a natural part of their growth - and only the mightiest of the lords of Hell could produce such a creature, such as the Four Winds who were sired when Adorjan lay with a Solar in his dreams. Moreover, these progeny are children, and thus will not begin life at the full of their power. To achieve their full potential, they will require a nurturing childhood, exotic reagents which strengthen their natural essence, the appropriate diet, and so on.
There are no easter eggs in these rules. If you believe you have found a way to produce offspring who are more powerful and easier to produce than Terrestrials and who can self-replicate, you have found something which goes against design intent and which needs to be fixed. In the High First Age, the Solar Exalted struggled to produce their lineages of golden children and failed to develop something superior to the Terrestrial Exalted. Players will have no more success than them.
Solars - The Golden Children
Shining and brilliant, the golden children are gods born into perfected human flesh. Though they are material and do not need a role from the Celestial Bureaucracy to define themselves, they lack the dual-souled nature of mankind. Their incorruptible flesh never ages past adulthood, and even the most grievous injury will heal in time, if it does not kill them. They have some of the raw brilliance of their parents, even if they lack the power of the Terrestrial Exalted. By the decree of the Sun, every golden child born automatically is assigned a role as one of his handmaidens or pages - though even in the High First Age, his detachment from the world meant this role was mostly ceremonial and they were left to do as they wish. Long ago, the Golden Queen of An Teng was one of these gods wrapped in mortal flesh. In the Usurpation, the Terrestrials killed every one of them they could find, out of revenge and the fear they would be the nexus of any rebellion against their coup.
Alas, such perfection comes at a cost. Golden children only reproduce with great difficulty. The hopes of the Solar god-kings of the first age for their own dynasties came to little. Even with the greatest minds of the Twilight caste thrown behind resolving these issues, most of the get of the golden children were godblooded - human, fallible and aging. A few ruinously expensive bloodlines were created, requiring huge expenditures of essence, medical manses built with the greatest medical arts of the High First Age and frequent cross-breeding of Solars back into these lines. The Twilights bragged that some day they would overcome such issues. It is certainly true that many of the Terrestrials feared this, and the idea that the Solars were seeking to replace them led many Gens to throw their support behind the Great Rebellion.
Golden children may learn Solar Excellencies, and use a dice cap of (Ability + Attribute). They also learn Spirit Charms, themed around the sun and human brilliance. They calculate their mote pools as gods. They are rarely born with any major divergence from the human form, though they express their nature in many more subtle ways. A golden child with four arms is not unheard of, however.
Lunars - The Moon-Touched
While the children of Solars are glorious Apollonian heroes, the Lunars spawn Dionysian tricksters. Sometimes their children are out-and-out monsters; quicksilver dragons, giants who tower over the trees, white wolves as large as a yeddim. Most of the time, though, they are bright-eyed children who change their forms as you might change your clothes. Many have observed that the moontouched have too much of Luna in them to feel comfortable - and Luna would seem to agree. Her beloved grandchildren formally are assigned to her service, but she never gives them any direct orders - instead preferring to let them loose in Creation.
Unlike the golden children, the moon-touched have no problems with fertility. However, the further they get from their Exalted parent, the weaker they become as the trickster power of the moon seeps from their veins. Within a generation or two, the moon-touched merely have godblooded children, forming lines that mix the blood of men and monsters. Sometimes a true moontouched will show up in such a bloodline unpredictably.
Moreover, a moon-touched child is a great investment. Lunars who have thought to breed themselves an army through use of animals which have many offspring have wound up disappointed, for spreading their seed like that spread it thinly. Many of the armies of the Silver Pact are led by a moon-touched - and when Terrestrials kill them, it can produce bloated counts of slain Lunar anathema.
The moontouched may learn Lunar Excellencies, and use a dice cap of (Attribute + Enlightenment / 2) or (Enlightenment), whichever is lower. They also learn Spirit Charms, themed around the moon, madness, monstrosity and other Lunar themes. They calculate their mote pools as gods. Moontouched children are often radically inhuman - commonly having at least (sum of parents' Enlightenment) mutation points, usually distributed between multiple forms.
Sidereals - The Starborn
The blood of the Sidereals runs true in the starborn. It is plain to see that they have their Exalted parent's eyes. Their thread runs through their Maiden's firm grasp, and their existence is twisted towards a single goddess' domain.
All starborn automatically on birth recieve a role in the Bureau of Destiny, personally attached to the Maiden whose nature defines them. Unlike the golden children and the moon-touched, the Maidens are much more active in making use of their servants and starborn will often find themselves run ragged handling less important missions when a Sidereal cannot be spared. Throughout Creation, starborn handle much of the long-term placements and infrastructural work for the Sidereal Exalted. They maintain front organisations, monitor demon cults and ensure that there are convenient identities for a Sidereal to slip into. Despite the way that they are little different from gods - and their children are always godblooded - there is a subtle discrimination against them, which is why they tend to get so many missions in Creation.
The children of the Sidereals are gods in human flesh and the adopted children of the Maidens. Though their flesh is not unaging or incorruptible, their immortal spirit lives on past the death of their flesh. When a starborn 'dies', they leave their mortal flesh and become an immaterial divine presence. This is generally considered to be quite an annoyance, especially if they were in the middle of something, and most petition the Bureau of Destiny to grant them a new body. As long as they have a good record, this is usually issued within a few years - during which they are stuck in Heaven doing paperwork. Some dry wits have observed that this must be much what like the River Lethe feels like.
Starborn may learn Sidereal Excellencies, and use the Sidereal dice cap. They may make use of Resplendent Destinies. They may also learn Spirit Charms, with the same themes as their Sidereal parent's Maiden. In the case where a starborn has two Sidereal parents, they have heterochromia and may learn both Maidens' Spirit Charms - and also have two Departments they must report to. Starborn are often striking, but mutations they possess are usually hidden or purely sensory to give them an unusual look at the world - like the blue-eyed starborn who can smell out love or lust.
Infernals - The Akuma
Long before Creation, the first akuma were born - though they bore a different name in those times. The akuma are the creatures of the Primordials, who exist within their Mythoi but who do not descend from them. They are not the tool-races of the first circle, and exist for their own purposes. Many of them were slain in the Primordial War, and only a few of them - called behemoths by some - exist within Malfeas to this day. The most famous akuma are the Four Winds, daughters of Adorjan, but others exist.
The Green Sun Princes shall find, too, that their own legends produce creatures born of their glory. Born of their flesh and souls, their akuma-children shall sit at their left hand, surrounded by their spawn-races. Their forms and their natures shall be determined by the legends of their parents, reinterpreting the old stories of the Primordials to new forms. Babes whose flesh is shadows and whose eyes burn with green fire will play with children with the form of ten-legged glass tigers.
Some akuma form breeds, new races in and among themselves. Given time, they will scurry across the surface of Creation in their thousands. Others are unique monstrosities - wasps the size of a yeddim with a human torso in place of their head, giants with brass arms that can tear down a city wall, wolves that seek to eat the gods and snakes who hate the Pole of Wood. It all depends on the Yozi metabiology that their parent has infused into themselves and what they sculpt their child to be.
Akuma are diverse beyond belief. The weakest of them are little different from a mortal child, born as a creature of an alien reality. More powerful ones might have the power of a strong first circle demon - and those ones are much of a likeness with the other progeny above - while the very strongest are weapons grown by their parents, little different from city-destroying golem built by a Solar god-king. Their themes will derive from their parents' and the exotic ingredients fed to them during gestation and childhood.
Abyssals - A Dead Branch
As with all other Celestials, the Abyssal Exalted find that their progeny are suffused by with their power. Unfortunately for the dead princes, they draw from the coldness of death and the hungry well of Oblivion - and both are anathema to new life.
Abyssal Exalted whose power grows too much are sterile. There is too much death in them to create. Even when they manage - beyond hope - to conceive a child, a miscarriage invariably ensues. Oblivion brings no new life and no new beginnings. When a mortal carries the child, the complications may threaten their life too.
An Abyssal who has sired or mothered such a failed pregnancy may find foetal monstrosities within the Labyrinth that wail and scream for them. Perhaps they are just a manifestation of how that nightmare realm feeds on their guilt and takes form to torment them. Or perhaps the whispering horrors of the bloody depths truly are their never-born children.
A Note on Dragonblooded
Celestial Exalts always count as pure mortals for the purposes of Dragonblooded breeding. It doesn't matter if they had an unimpeachable line of ancestry and bemused the Realm when they didn't Exalt despite their clear aspect markings. Once they take their Second Breath that all burns away and they're worth nothing more than a random Threshold peasant.
In fact, given the extent to which the lines of the Dragon have spread over time, the average Threshold peasant counts for slightly more. After all, the peasant will carry some trace of Dragonblood back in their heritage, but the Celestial Exalt has had it all stripped away. The beginning of the decay of the bloodlines of the Terrestrials can be traced back to Celestial Exalted who refused to let the Gens do as their laws stated they should, and dispose of such half-breed children. Had the Terrestrials been permitted to put duty above obligation and love, perhaps the history of Creation might be very different. The same applies to all other inhuman would-be parents. God, demon, faerie, elemental - if they lack the Dragons' blood, they serve only to weaken the chance of Terrestrial Exaltation.
The sole exception to this are the Elemental Dragons themselves. Rumour has it that if a Dragonblood were to couple with them - and survive the experience - a child produced from such a union would be a Dragonblood akin to those in the very beginning, lacking any impurities in their blood. Some have whispered that Princess Vanefa may be one of these children - though whether such tales are intended to cast doubt on the Empress' fidelity or praise her for impressing Sextes Jylis are unclear. And anyway, most believe that the strength of her blood comes from the Fourth Empress' choice for her second husband and that such tales are intended to force a divide between the Imperial Household and House Cynis.