Are there any Infinite Combos in Monster Train?

Yes, there are infinite combos in Monster Train.

Here's an illustrative Example of one I remember pulling off at least once, so it's feasible if rare at Covenant 25, and not merely a pathological example:

1. Have your champion be Little Fade, give it at least one level of Fire Light.
2. Play with the Stygian Guard as your secondary clan.
3. Get two copies of Offering Monument. (It doesn't need upgrades, but Quick can help before the combo pops off completely).
4. Get a copy of the card Intent on Death (IOD) from your first combat.
5. Lower its cost down to zero in the first two floors using the Magic shop (or on the first floor using a lucky refresh and cash bonuses from Collector and Challenge), or using a Valuestone if using the DLC.
6. Encounter the event that allows you to copy this card six times (not necessary, but quite helpful in making the infinite easier). Note: A patch made it so this Event can only be encountered early in the game.
7. Optional: Find the Artifact Waxer Snuffer "Extinguish abilities are triggered twice" for unlimited health as well.
8. Remove as many cards from the deck that aren't Offering Monument or Intent on Death as possible.

The combo works because each copy played of Intent on Death will draw you two cards immediately, allowing you to continue playing them, and ends up giving your monuments unbounded additional attack. As long as you have enough copies in the deck, that is, given your hand size H, the number of non-IOD's X <= 9, and the number of IODs (I) satisfies I >= 2, I >= X - H, then you can draw all your non-IODs in your hand and continue playing Intent on Death an arbitrary amount of times on Little Fade. Each Intent on Death played increases the Attack value of the Monuments, while keeping their health the same (or granting 5 hp if you have the Artifact Waxer Snuffer).

Enjoy one-shotting the Seraph with your big monuments of unlimited power.

Here's a nice simple one. Two Deep Offering with consume removed, Kinstone Totem, and a way to consume all but 6 cards of your deck. That leaves room for two deadweights and another card.

Deep offering will, for 3 pyre, give you 4 pyre and redraw a hand of 2 deadweights, Deep Offering, and the other card. You can play Deep Offering as many times as you like.

This gives you infinite energy- if the sixth card is an x cost, you can one-shot bosses with it. It also gives you infinite Incant triggers.

This combo surprisingly practical. Everything is from a single clan and it only requires a relic and two copies of a card. An extremely lucky player can pursue it from the start of the game if they get Deep Offering in their starting deck and Kinstone Totem as their starting artifact.

Note that this combo does not work on Seraph the Chaste on covenant 17+ due to the vengeful shards.