Leases - Schedule of Components of Lease Expense (Details) - USD ($) $ in Millions	3 Months Ended
Mar. 31, 2025	Mar. 31, 2024
Finance lease cost:
Amortization of right-of-use assets	$ 0.1	$ 0.1
Net finance lease cost	0.1	0.1
Operating lease cost	4.2	4.5
Variable lease cost	0.2	0.1
Sublease income	0.0	(0.2)
Total non-current lease cost	4.5	4.5
Short-term lease costs	8.0	7.2
Total lease cost	$ 12.5	$ 11.7

Amount of amortization expense attributable to right-of-use asset from finance lease.

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-4

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_FinanceLeaseRightOfUseAssetAmortization
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of lease cost recognized by lessee for lease contract.

+ References

+ Details

Name:	us-gaap_LeaseCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of single lease cost, calculated by allocation of remaining cost of lease over remaining lease term. Includes, but is not limited to, single lease cost, after impairment of right-of-use asset, calculated by amortization of remaining right-of-use asset and accretion of lease liability.

+ References

+ Details

Name:	us-gaap_OperatingLeaseCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of short-term lease cost, excluding expense for lease with term of one month or less.

+ References

+ Details

Name:	us-gaap_ShortTermLeaseCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of sublease income excluding finance and operating lease expense.

+ References

+ Details

Name:	us-gaap_SubleaseIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of variable lease cost, excluded from lease liability, recognized when obligation for payment is incurred for finance and operating leases.

+ References

+ Details

Name:	us-gaap_VariableLeaseCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Components Of Finance Lease Cost

+ References

No definition available.

+ Details

Name:	vate_ComponentsOfFinanceLeaseCostAbstract
Namespace Prefix:	vate_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Finance Lease, Cost

+ References

No definition available.

+ Details

Name:	vate_FinanceLeaseCost
Namespace Prefix:	vate_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Lease Cost, Non Current

+ References

No definition available.

+ Details

Name:	vate_LeaseCostNonCurrent
Namespace Prefix:	vate_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration