EX-10.4

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Exhibit 10.4

AVALYN PHARMA INC.

2026 EMPLOYEE STOCK PURCHASE PLAN

The purpose of the Avalyn Pharma Inc. 2026 Employee Stock Purchase Plan (the “Plan”) is to provide eligible employees of Avalyn Pharma Inc. (the “Company”) and each Designated Company (as defined in Section 11) with opportunities to purchase shares of the Company’s common stock, par value $0.001 per share (the “Common Stock”). 370,000 shares of Common Stock in the aggregate have been approved and reserved for this purpose, plus on January 1, 2027 and each January 1 thereafter until the Plan terminates pursuant to Section 20, the number of shares of Common Stock reserved and available for issuance under the Plan shall be cumulatively increased by the least of (i) 740,000 shares of Common Stock, (ii) 1% of the number of Outstanding Shares on the immediately preceding December 31, and (iii) such lesser number of shares of Common Stock as determined by the Administrator (as defined in Section 1).

The Plan includes two components: a Code Section 423 Component (the “423 Component”) and a non-Code Section 423 Component (the “Non-423 Component”). It is intended for the 423 Component to constitute an “employee stock purchase plan” within the meaning of Section 423(b) of the U.S. Internal Revenue Code of 1986, as amended (the “Code”), and the 423 Component shall be interpreted in accordance with that intent. Under the Non-423 Component, which does not qualify as an “employee stock purchase plan” within the meaning of Section 423(b) of the Code, options will be granted pursuant to rules, procedures or sub-plans adopted by the Administrator designed to comply with applicable laws to achieve tax and other objectives. Except as otherwise provided herein or by the Administrator, the Non-423 Component will operate and be administered in the same manner as the 423 Component. Unless otherwise defined herein, capitalized terms in this Plan shall have the meaning ascribed to them in Section 11.

Administration. The Plan will be administered by the person or persons (the “Administrator”) appointed by the Company’s Board of Directors (the “Board”) for such purpose. The Administrator has authority at any time to: (i) adopt, alter and repeal such rules, guidelines and practices for the administration of the Plan and for its own acts and proceedings as it shall deem advisable; (ii) interpret the terms and provisions of the Plan, including to accommodate the specific requirements of applicable laws, regulations and procedures in jurisdictions outside of the United States; (iii) make all determinations it deems advisable for the administration of the Plan; (iv) decide all disputes arising in connection with the Plan; and (v) otherwise supervise the administration of the Plan. All interpretations and decisions of the Administrator shall be binding on all persons, including the Company and the Participants. No member of the Board or individual exercising administrative authority with respect to the Plan shall be liable for any action or determination made in good faith with respect to the Plan or any option granted hereunder.

Offerings. The Company will make one or more offerings to eligible employees to purchase Common Stock under the Plan (“Offerings”) consisting of one or more Purchase Periods. Each Offering will begin and end on the dates to be determined by the Administrator, provided that no Offering shall exceed 27 months in duration. Unless the Administrator, in its sole discretion, chooses otherwise prior to an Offering Date (as defined below), and to the extent an Offering has more than one Purchase Period and to the extent permitted by applicable law, if the Fair Market Value of the Common Stock on any Exercise Date in an Offering is lower than the Fair Market Value of the Common Stock on the Offering Date, then all participants in such Offering automatically will be withdrawn from such Offering immediately after the exercise of their option on such Exercise Date and automatically re-enrolled in the immediately following Offering as of the first day thereof and the preceding Offering will terminate.

Eligibility. All individuals classified as employees on the payroll records of the Company and each Designated Company are eligible to participate in any one or more of the Offerings under the Plan, provided that, the Administrator may determine, in advance of any Offering, that employees are eligible only if, as of the first day of the applicable Offering (the “Offering Date”) (a) they are customarily employed by the Company or a Designated Company for more than 20 hours a week (or such lesser number of hours per week consistent with Section 423 of the Code), (b) they are customarily employed by the Company or a Designated Company for more than five months per calendar year, (c) they have completed such minimum period of service prior to the Offering Date (provided such service requirement does not exceed two years of employment), and/or (d) they satisfy such other criteria as the Administrator may determine consistent with Section 423 of the Code. Notwithstanding any other provision herein, individuals who are not contemporaneously classified as employees of the Company or a Designated Company for purposes of the Company’s or applicable Designated Company’s payroll system are not considered to be eligible employees of the Company or any Designated Company and shall not be eligible to participate in the Plan. In the event any such individuals are reclassified as employees of the Company or a Designated Company for any purpose, including, without limitation, common law or statutory employees, by any action of any third party, including, without limitation, any government agency, or as a result of any private lawsuit, action or administrative proceeding, such individuals shall, notwithstanding such reclassification, remain ineligible for participation. Notwithstanding the foregoing, the exclusive means for individuals who are not contemporaneously classified as employees of the Company or a Designated Company on the Company’s or Designated Company’s payroll system to become eligible to participate in this Plan is through an amendment or subplan to this Plan, duly executed by the Company, which specifically renders such individuals eligible to participate herein.

Participation.

(a)

Participation in Offerings. An eligible employee who is not a Participant in any prior Offering may participate in a subsequent Offering by submitting an enrollment form to the Company or an agent designated by the Company (in the manner described in Section 4(b) at least 15 business days before the Offering Date (or by such other deadline as shall be established by the Administrator for the Offering).

(b)

Enrollment. The enrollment form (which may be in an electronic format or such other method as determined by the Company in accordance with the Company’s practices) will (a) state a whole percentage or amount to be deducted from an eligible employee’s Compensation (as defined in Section 11) per pay period, (b) authorize the purchase of Common Stock in each Offering in accordance with the terms of the Plan and (c) specify the exact name or names in which shares of Common Stock purchased for such individual are to be issued pursuant to Section 10. An employee who does not enroll in accordance with these procedures will be deemed to have waived the right to participate. Unless a Participant files a new enrollment form or withdraws from the Plan, such Participant’s deductions or contributions and purchases will continue at the same percentage or amount of Compensation for future Offerings, provided he or she remains eligible.

(c)

Notwithstanding the foregoing, participation in the Plan will neither be permitted nor be denied contrary to the requirements of the Code.

Employee Contributions. Each eligible employee may authorize payroll deductions or contributions at a minimum of 1 percent (1%) up to a maximum of 15 percent (15%) of such employee’s Compensation for each pay period or such other maximum as may be specified by the Administrator in advance of an Offering. The Company will maintain book accounts showing the amount of payroll deductions or contributions made by each Participant for each Purchase Period within an Offering. No interest will accrue or be paid on payroll deductions or contributions, except as may be required by applicable law. If payroll deductions or contributions for purposes of the Plan are prohibited or otherwise problematic under applicable law (as determined by the Administrator in its discretion), the Administrator may require Participants to contribute to the Plan by such other means as determined by the Administrator. Any reference to “payroll deductions” or contributions in this Section 5 (or in any other section of the Plan) will similarly cover contributions by other means made pursuant to this Section 5.

Deduction Changes. Except as may be determined by the Administrator in advance of an Offering, a Participant may not increase or decrease his or her payroll deduction or contributions during any Offering, but may increase or decrease his or her payroll deduction or contributions with respect to the next Offering (subject to the limitations of Section 5) by filing a new enrollment form at least fifteen (15) business days before the next Offering Date (or by such other deadline as shall be established by the Administrator for the Offering). The Administrator may, in advance of any Offering, establish rules permitting a Participant to increase, decrease or terminate his or her payroll deduction or contributions during an Offering.

Withdrawal. A Participant may withdraw from participation in the Plan by delivering a written notice of withdrawal to the Company or an agent designated by the Company (in accordance with such procedures as may be established by the Administrator). The Participant’s withdrawal will be effective as of the next business day (or such other date established by the Administrator). Following a Participant’s withdrawal, the Company will promptly refund such individual’s entire account balance under the Plan to him or her (after payment for any Common Stock purchased before the effective date of withdrawal). Partial withdrawals are not permitted. Such an employee may not begin participation again during the remainder of the Offering, but may enroll in a subsequent Offering in accordance with Section 4.

Grant of Options. On each Offering Date, the Company will grant to each eligible employee who is then a Participant in the Plan an option (“Option”) to purchase, on the last day of a Purchase Period (an “Exercise Date”) and at the Option Price (as defined herein) hereinafter provided for, the lower of (a) a number of shares of Common Stock determined by dividing such Participant’s accumulated payroll deductions or contributions on such Exercise Date by the Option Price, or (b) a number of shares of Common Stock determined by dividing $25,000 by the Fair Market Value of the Common Stock on the Offering Date for such Offering (or such other maximum number of shares as shall have been established by the Administrator in advance of the Offering); provided, however, that such Option shall be subject to the limitations set forth below. Each Participant’s Option shall be exercisable only to the extent of such Participant’s accumulated payroll deductions or contributions on the Exercise Date. The purchase price for each share purchased under each Option (the “Option Price”) will be 85 percent (85%) of the Fair Market Value (as defined in Section 11) of the Common Stock on the Offering Date or the Exercise Date, whichever is less.

Notwithstanding the foregoing, no Participant may be granted an Option hereunder if such Participant, immediately after the Option was granted, would be treated as owning stock possessing 5 percent (5%) or more of the total combined voting power or value of all classes of stock of the Company or any Parent or Subsidiary (as defined in Section 11). For purposes of the preceding sentence, the attribution rules of Section 424(d) of the Code shall apply in determining the stock ownership of a Participant, and all stock which the Participant has a contractual right to purchase shall be treated as stock owned by the Participant. In addition, no Participant may be granted an Option which permits his or her rights to purchase stock under the Plan, and any other employee stock purchase plan of the Company and its Parents and Subsidiaries, to accrue at a rate which exceeds $25,000 of the Fair Market Value of the Common Stock (determined on the option grant date or dates) for each calendar year in which the Option is outstanding at any time. The purpose of the limitation in the preceding sentence is to comply with Section 423(b)(8) of the Code and shall be applied taking Options into account in the order in which they were granted.

Exercise of Option and Purchase of Shares. Each employee who continues to be a Participant in the Plan on an Exercise Date shall be deemed to have exercised his or her Option on such date and shall acquire from the Company such number of whole shares of Common Stock reserved for the purpose of the Plan as his or her accumulated payroll deductions on such date will purchase at the Option Price, subject to any other limitations contained in the Plan. Unless otherwise determined by the Administrator in advance of an Offering, any amount remaining in a Participant’s account after the purchase of shares on an Exercise Date of an Offering solely by reason of the inability to purchase a fractional share will be carried forward to the next Purchase Period; provided, that if such Exercise Date is the final Exercise Date of an Offering, such amount will be carried forward to the next Offering and any other balance remaining in a Participant’s account at the end of an Offering will be refunded to the Participant promptly.

10.

Issuance of Certificates. Certificates or book-entries at the Company’s transfer agent representing shares of Common Stock purchased under the Plan may be issued only in the name of the employee, in the name of the employee and another person of legal age as joint tenants with rights of survivorship or in the name of a broker authorized by the employee to be his, her or their nominee for such purpose.

11.

Definitions.

The term “Affiliate” means any entity that, directly or indirectly through one or more intermediaries, controls, is controlled by or is under the common control with, the Company.

The term “Compensation” means the amount of base pay, prior to salary reduction pursuant to Sections 125, 132(f) or 401(k) of the Code, but excluding overtime, commissions, incentive or bonus awards, allowances and reimbursements for expenses such as relocation allowances or travel expenses, income or gains related to Company stock options or other share-based awards and similar items. The Administrator shall have the discretion to determine the application of this definition to Participants outside the United States.

The term “Designated Company” means any present or future Subsidiary or Affiliate that has been designated by the Administrator to participate in the Plan. The Administrator may so designate any Subsidiary or Affiliate, or revoke any such designation, at any time and from time to time, either before or after the Plan is approved by the stockholders, and may further designate such companies or Participants as participating in the 423 Component or the Non-423 Component. The Administrator may also determine which Affiliates or eligible employees may be excluded from participation in the Plan, to the extent consistent with Section 423 of the Code or as implemented under the Non-423 Component, and determine which Designated Company or Companies will participate in separate Offering (to the extent that the Company makes separate Offerings). For purposes of the 423 Component, only the Company and its Subsidiaries may be Designated Companies; provided; however, that at any given time, a Subsidiary that is a Designated Company under the 423 Component will not be a Designated Company under the Non-423 Component. The current list of Designated Companies is attached hereto as Appendix A.

The term “Fair Market Value of the Common Stock” on any given date means the fair market value of the Common Stock determined in good faith by the Administrator; provided, however, that if the Common Stock is admitted to quotation on the National Association of Securities Dealers Automated Quotation System (“Nasdaq”), Nasdaq Global Market, The New York Stock Exchange or another national securities exchange or traded on any established market, the determination shall be made by reference to the closing price on such date. If there is no closing price for such date, the determination shall be made by reference to the last date preceding such date for which there is a closing price.

The term “Initial Public Offering” means the first underwritten, firm commitment public offering pursuant to an effective registration statement under the Securities Act of 1933, as amended, covering the offer and sale by the Company of its Common Stock.

The term “New Exercise Date” means a new Exercise Date if the Administrator shortens any Offering then in progress.

The term “Outstanding Shares” means, as of a specified date, the sum of (a) the number of shares of Stock issued and outstanding and (b) the number of shares of Stock issuable pursuant to the exercise of any outstanding, pre-funded warrants to acquire Stock for a nominal exercise price.

The term “Parent” means a “parent corporation” with respect to the Company, as defined in Section 424(e) of the Code.

The term “Participant” means an individual who is eligible as determined in Section 3 and who has complied with the provisions of Section 4.

The term “Purchase Period” means a period of time specified within an Offering, as may be specified by the Administrator in accordance with Section 2, generally beginning on the Offering Date or the next day following an Exercise Date within an Offering, and ending on an Exercise Date. An Offering may consist of one or more Purchase Periods.

The term “Registration Date” means the date on which the registration statement on Form S-1 is filed by the Company with respect to its Initial Public Offering is declared effective by the U.S. Securities and Exchange Commission (the “SEC”).

The term “Sale Event” means (i) the sale of all or substantially all of the assets of the Company on a consolidated basis to an unrelated person or entity, (ii) a merger, reorganization, statutory share exchange, consolidation, or similar transaction pursuant to which the holders of the Company’s outstanding voting power and outstanding stock immediately prior to such transaction do not own a majority of the outstanding voting power and outstanding stock or other equity interests of the resulting or successor entity (or its ultimate parent, if applicable) immediately upon completion of such transaction, (iii) the sale of all of the Common Stock to an unrelated person, entity or group thereof acting in concert, (iv) any other transaction in which the owners of the Company’s outstanding voting power immediately prior to such transaction do not own at least a majority of the outstanding voting power of the Company or any successor entity immediately upon completion of the transaction other than as a result of the acquisition of securities directly from the Company, or (v) the approval by the stockholders of the Company of a complete liquidation or dissolution of the Company.

The term “Subsidiary” means a “subsidiary corporation” with respect to the Company, as defined in Section 424(f) of the Code.

12.

Rights on Termination of Employment. If a Participant’s employment terminates for any reason before the Exercise Date for any Offering, no payroll deduction or contributions will be taken from any pay due and owing to the Participant and the balance in the Participant’s account will be paid to such Participant or, in the case of such Participant’s death, if permitted by the Administrator and valid under applicable law, to his or her designated beneficiary or to the legal representative of his or her estate as if such Participant had withdrawn from the Plan under Section 7. An employee will be deemed to have terminated employment, for this purpose, if the corporation that employs him or her, having been a Designated Company, ceases to be a Subsidiary or Affiliate, or if the employee is transferred to any corporation other than the Company or a Designated Company. Unless otherwise determined by the Administrator, a Participant whose employment transfers between, or whose employment terminates with an immediate rehire (with

no break in service) by, Designated Companies or a Designated Company, then the Company will not be treated as having terminated Participant’s employment for purpose of participating in the Plan or an Offering; provided, however, that if a Participant transfers from an Offering under the 423 Component to an Offering under the Non-423 Component, the exercise of the Participant’s Option will be qualified under the 423 Component only to the extent that such exercise complies with Section 423 of the Code. If a Participant transfers from an Offering under the Non-423 Component to an Offering under the 423 Component, the exercise of the Participant’s Option will remain non-qualified under the Non-423 Component. Further, an employee will not be deemed to have terminated employment for purposes of this Section 12 if the employee is on an approved leave of absence for military service or sickness or for any other purpose approved by the Company, if the employee’s right to reemployment is guaranteed either by a statute or by contract or under the policy pursuant to which the leave of absence was granted or if the Administrator otherwise provides in writing.

13.

Special Rules and Sub-Plans. Notwithstanding anything herein to the contrary, the Administrator may adopt special rules or sub-plans applicable to the employees of a particular Designated Company, whenever the Administrator determines that such rules are necessary or appropriate for the implementation of the Plan in a jurisdiction where such Designated Company has employees, regarding, without limitation, eligibility to participate in the Plan, handling and making of payroll deductions or contributions by other means, establishment of bank or trust accounts to hold payroll deductions or contributions, payment of interest, conversion of local currency, obligation to pay payroll tax, withholding procedures and handling of share issuances, any of which may vary according to applicable requirements; provided that if such special rules or sub-plans are inconsistent with the requirements of Section 423(b) of the Code, the employees subject to such special rules or sub-plans will participate in the Non-423 Component.

14.

Optionees Not Stockholders. Neither the granting of an Option to a Participant nor the deductions or contributions from his or her pay shall result in such Participant becoming a holder of the shares of Common Stock covered by an Option under the Plan until such shares have been purchased by and issued to him or her.

15.

Rights Not Transferable. Rights under the Plan are not transferable by a Participant other than by will or the laws of descent and distribution, and are exercisable during the Participant’s lifetime only by the Participant.

16.

Application of Funds. All funds received or held by the Company under the Plan may be combined with other corporate funds and may be used for any corporate purpose, unless otherwise required under applicable law.

17.

Adjustment in Case of Changes Affecting Common Stock. In the event of a subdivision of outstanding shares of Common Stock, the payment of a dividend in Common Stock or any other change affecting the Common Stock, the number of shares approved for the Plan and the share limitation set forth in Section 8 shall be equitably or proportionately adjusted to give proper effect to such event. In the case of and subject to the consummation of a Sale Event, the Administrator, in its discretion, and on such terms and conditions as it deems appropriate, is hereby authorized to take any one or more of the following actions whenever the Administrator determines that such action is appropriate in order to prevent the dilution or enlargement of the benefits or

potential benefits intended to be made available under the Plan or with respect to any right under the Plan or to facilitate such transactions or events:

(a)

To provide for either (i) termination of any outstanding Option in exchange for an amount of cash, if any, equal to the amount that would have been obtained upon the exercise of such Option had such Option been currently exercisable or (ii) the replacement of such outstanding Option with other options or property selected by the Administrator in its sole discretion.

(b)

To provide that the outstanding Options under the Plan shall be assumed by the successor or survivor corporation, or a parent or subsidiary thereof, or shall be substituted for similar options covering the stock of the successor or survivor corporation, or a parent or subsidiary thereof, with appropriate adjustments as to the number and kind of shares and prices.

(c)

To make adjustments in the number and type of shares of Common Stock (or other securities or property) subject to outstanding Options under the Plan and/or in the terms and conditions of outstanding Options and Options that may be granted in the future.

(d)

To provide that the Offering with respect to which an Option relates will be shortened by setting a New Exercise Date on which such Offering will end. The New Exercise Date will occur before the date of the Sale Event. The Administrator will notify each Participant in writing or electronically prior to the New Exercise Date, that the Exercise Date for the Participant’s Option has been changed to the New Exercise Date and that the Participant’s Option will be exercised automatically on the New Exercise Date, unless prior to such date the Participant has withdrawn from the Offering as provided in Section 7 hereof.

(e)

To provide that all outstanding Options shall terminate without being exercised and all amounts in the accounts of Participants shall be promptly refunded.

18.

Amendment of the Plan. The Board may at any time and from time to time amend the Plan in any respect, except that without the approval within 12 months of such Board action by the stockholders, no amendment shall be made increasing the number of shares approved for the Plan or making any other change that would require stockholder approval in order for the Section 423 Component of the Plan, as amended, to qualify as an “employee stock purchase plan” under Section 423(b) of the Code.

19.

Insufficient Shares. If the total number of shares of Common Stock that would otherwise be purchased on any Exercise Date plus the number of shares purchased under previous Offerings under the Plan exceeds the maximum number of shares issuable under the Plan, the shares then available shall be apportioned among Participants in proportion to the amount of payroll deductions or contributions accumulated on behalf of each Participant that would otherwise be used to purchase Common Stock on such Exercise Date.

20.

Termination of the Plan. The Plan may be terminated at any time by the Board. Upon termination of the Plan, all amounts in the accounts of Participants shall be promptly refunded. Unless terminated earlier, the Plan shall expire on the ten-year anniversary of the Registration Date.

21.

Governmental Regulations. The Company’s obligation to sell and deliver Common Stock under the Plan is subject to applicable laws and the completion of any registration or qualification of the Common Stock under any U.S. or non-U.S., local, state or federal securities or exchange control law, or under rulings or regulations of the SEC or of any other governmental regulatory body, and to obtaining any approval or other clearance from any U.S. or non-U.S. local, state or federal governmental agency, which registration, qualification or approval the Company shall, in its absolute discretion, deem necessary or advisable. The Company is under no obligation to register or qualify the Common Stock with the SEC or any other U.S. or non-U.S. securities commission or to seek approval or clearance from any governmental authority for the issuance or sale of such stock.

22.

Governing Law. This Plan and all Options and actions taken thereunder shall be governed by, and construed in accordance with, the General Corporation Law of the State of Delaware as to matters within the scope thereof, and as to all other matters shall be governed and construed in accordance with the internal laws of the State of Delaware, applied without regard to conflict of law principles.

23.

Issuance of Shares. Shares may be issued upon exercise of an Option from authorized but unissued Common Stock, from shares held in the treasury of the Company or from any other proper source.

24.

Tax Withholding. Participation in the Plan is subject to any applicable U.S. and non-U.S. federal, state or local tax withholding requirements on income the Participant realizes in connection with the Plan. Each Participant agrees, by entering the Plan, that the Company or any Subsidiary or Affiliate may withhold from a Participant’s wages, salary or other compensation at any time the amount necessary for the Company or any Subsidiary or Affiliate to meet applicable withholding obligations, including any withholding required to make available to the Company or any Subsidiary or Affiliate any tax deductions or benefits attributable to the sale or disposition of Common Stock by such Participant. In addition, the Company or any Subsidiary or Affiliate may withhold from the proceeds of the sale of Common Stock or use any other method of withholding that the Company or any Subsidiary or Affiliate deems appropriate to the extent permitted by U.S. Treasury Regulation Section 1.423-2(f) with respect to the 423 Component. The Company will not be required to issue any Common Stock under the Plan until such obligations are satisfied.

25.

Notification Upon Sale of Shares Under the 423 Component. Each Participant agrees, by entering the 423 Component of the Plan, to give the Company prompt notice of any disposition of shares purchased under the Plan where such disposition occurs within two years after the date of grant of the Option pursuant to which such shares were purchased or within one year after the date such shares were purchased.

26.

Effective Date and Approval of Shareholders. The Plan shall take effect on the date immediately preceding the Registration Date, subject to approval by the holders of a majority of the votes cast at a meeting of stockholders at which a quorum is present or by written consent of the stockholders (the “Effective Date”).

27.

Equal Rights and Privileges. Notwithstanding any provision of the Plan to the contrary and in accordance with Section 423 of the Code for the 423 Component of the Plan, all eligible employees who are granted Options under the Plan shall have the same rights and privileges.

28.

No Right to Continued Service. Neither the Plan nor any compensation paid hereunder will confer on any Participant the right to continue as an employee or in any other capacity.

29.

Entire Plan. This Plan constitutes the entire plan with respect to the subject matter hereof and supersedes all prior plans with respect to the subject matter hereof.

DATE APPROVED BY BOARD OF DIRECTORS: April 6, 2026

DATE APPROVED BY STOCKHOLDERS: April 22, 2026

APPENDIX A

Designated Companies

None