<PAGE>   1





                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549


                                 SCHEDULE 13G




                  Under the Securities Exchange Act of 1934
                            (Amendment No.   4   )
                                           -----



                              Unifi Incorporated
                  -----------------------------------------
                               (Name of Issuer)




                                    Common
                  -----------------------------------------
                        (Title of Class of Securities)




                                  904677101
                  -----------------------------------------
                                (CUSIP Number)



                              December 31, 1994
                  -----------------------------------------
           (Date of Event which Requires Filing of this Statement)



Check the following box if a fee is being paid with this statement  /  /






                                                                     Page 1 of 7

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<TABLE>
 <S>                                                                <C>
  (1)     Names of Reporting Persons S.S. or I.R.S.                 Wachovia Corporation
          Identification Nos. of Above Persons                      56-1473727

  (2)     Check the Appropriate Box if a Member of a Group (See     (a)     N/A
          Instructions)
                                                                    (b)     N/A
  (3)     SEC Use Only

  (4)     Citizenship or Place of Organization                      North Carolina

 Number of Shares      (5)     Sole Voting Power                    1,095,410.00
 Beneficially      
 Owned by Each         (6)     Shared Voting Power                  1,219,606.00
 Reporting Person 
 With                  (7)     Sole Dispositive Power               5,531,494.00
                   
                       (8)     Shared Dispositive Power                29,586.00

  (9)     Aggregate Amount Beneficially Owned by Each Reporting
          Person                                                    5,579,970.00

 (10)     Check if Aggregate Amount in Row 9 Excludes Certain
          Shares
          (See Instructions)

 (11)     Percent of Class Represented by Amount in Row 9                   7.9%

 (12)     Type of Reporting Person
          (See Instructions)                                                 HC
</TABLE>






                                                                     Page 2 of 7

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<TABLE>
 <S>                                                                <C>
  (1)     Names of Reporting Persons S.S. or I.R.S.                 Wachovia Bank of North Carolina, NA
          Identification Nos. of Above Persons                      56-0927594

  (2)     Check the Appropriate Box if a Member of a Group (See     (a)     N/A
          Instructions)
                                                                    (b)     N/A
  (3)     SEC Use Only

  (4)     Citizenship or Place of Organization                      United States

 Number of Shares      (5)     Sole Voting Power                      710,535.00
 Beneficially     
 Owned by Each         (6)     Shared Voting Power                  1,217,406.00
 Reporting Person
 With                  (7)     Sole Dispositive Power               5,147,869.00
                  
                       (8)     Shared Dispositive Power                25,061.00

  (9)     Aggregate Amount Beneficially Owned by Each Reporting
          Person                                                    5,189,620.00

 (10)     Check if Aggregate Amount in Row 9 Excludes Certain
          Shares
          (See Instructions)

 (11)     Percent of Class Represented by Amount in Row 9                   7.1%

 (12)     Type of Reporting Person
          (See Instructions)                                                 BK
</TABLE>






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<PAGE>   4


<TABLE>
<S>              <C>
Item 1 (a)       Name of Issuer:

                        Unifi Incorporated

Item 1 (b)       Address of Issuer's Principal Executive Offices:

                        P.O. Box 19109
                        Greensboro, NC  27419

Item 2 (a)       Name of Person Filing:

                 A.     Wachovia Corporation

                 B.     Wachovia Bank of North Carolina, NA

Item 2 (b)       Address of Principal Business Office:

                 A.     301 North Main Street
                        Winston-Salem, North Carolina 27150-3099

                 B.     301 North Main Street
                        Winston-Salem, North Carolina 27150-3099

Item 2 (c)       Citizenship:

                 A.     North Carolina

                 B.     United States

Item 2 (d)       Title of Class of Securities:

                        Common

Item 2 (e)       CUSIP Number:

                        904677101

Item 3           If this statement is filed pursuant to Rules 13d-1(b), or 13d-3(b), check whether the person filing is a:

                 (a)    ( )    Broker or Dealer registered under Section 15 of the Act

                 (b)    (X)    Bank as defined in Section 3(a)(6) of the Act
                               (Wachovia Bank of North Carolina, NA)

                 (c)    ( )    Insurance Company as defined in Section 3(a)(19) of the Act

                 (d)    ( )    Investment Company registered under Section 8 of the Investment Company Act

                 (e)    ( )    Investment Adviser registered under Section 203 of the Investment Advisers Act of 1940
</TABLE>






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<TABLE>
<S>       <C>    <C>    <C>    <C>                                    <C>                                       <C>
                 (f)    ( )    Employee Benefit Plan, Pension Fund which is subject to the provisions of the Employee Retirement 
                               Income Security Act of 1974 or Endowment Fund; see 240.13d-1(b)(1)(ii)(F)

                 (g)    (X)    Parent Holding Company, in accordance with 240.13d-1(b)(ii)(G) (Note: See Item 7)
                               (Wachovia Corporation)

                 (h)    ( )    Group, in accordance with 240.13d-1(b)(1)(ii)(H)


Item 4           Ownership.

                 If the percent of the class owned, as of December 31 of the year covered by the statement, or as of the last day of
                 any month described in Rule 13d-1 (b)(2), if applicable, exceeds five percent, provide the following information as
                 of that date and identify those shares which there is a right to acquire.

          A.     Wachovia Corporation

                 (a)       Amount Beneficially Owned:                    5,579,970.00 
                                                                      ---------------


                 (b)       Percent of Class:                                     7.9% 
                                                                      ---------------


                 (c)       Number of Shares as to which such person has:

                 (i)       Sole power to vote or to direct the vote                                                1,095,410.00 
                                                                                                                ---------------

                 (ii)      Shared power to vote or to direct the vote                                              1,219,606.00 
                                                                                                                ---------------

                 (iii)     Sole power to dispose or to direct the disposition of                                   5,531,494.00 
                                                                                                                ---------------

                 (iv)      Shared power to dispose or to direct the disposition of                                    29,586.00 
                                                                                                                ---------------


          B.     Wachovia Bank of North Carolina, NA

                 (a)       Amount Beneficially Owned:                    5,189,620.00 
                                                                      ---------------


                 (b)       Percent of Class:                                     7.1% 
                                                                      ---------------


                 (c)       Number of Shares as to which such person has:

                 (i)       Sole power to vote or to direct the vote                                                  710,535.00 
                                                                                                                ---------------

                 (ii)      Shared power to vote or to direct the vote                                              1,217,406.00 
                                                                                                                ---------------

                 (iii)     Sole power to dispose or to direct the disposition of                                   5,147,869.00 
                                                                                                                ---------------

                 (iv)      Shared power to dispose or to direct the disposition of                                    25,061.00 
                                                                                                                ---------------
</TABLE>






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<TABLE>
<S>              <C>
Item 5           Ownership of Five Percent or Less of a Class.
                 -------------------------------------------- 

                        N/A

Item 6           Ownership of More than Five Percent on Behalf of Another Person.
                 --------------------------------------------------------------- 

                        N/A

Item 7           Identification and Classification of the Subsidiary Which Acquired the Security Being Reported on By The Parent
                 ---------------------------------------------------------------------------------------------------------------
                 Holding Company.
                 --------------- 

                        The securities to which this report relates are held by Wachovia Bank of North Carolina, NA
                        and Wachovia Bank of Georgia, NA as trustees.  This filing should not be construed as an
                        admission that the trustees or their parent, Wachovia Corporation, are, for the purposes of
                        Section 13(d) or 13(g) of the Act, beneficial owners of any securities covered by this
                        statement.

Item 8           Identification and Classification of Members of The Group.
                 --------------------------------------------------------- 

                        N/A

Item 9           Notice of Dissolution of Group.
                 ------------------------------ 

                        N/A

Item 10          Certification:
                 ------------- 

                 By signing below, I certify that, to the best of my knowledge and belief, the securities referred to above
                 were not acquired for the purpose of and do not have the effect of changing or influencing the control of the
                 issuer of such securities and were not acquired in connection with or as a participant in any transaction having
                 such purposes or effect.
</TABLE>


                                         SIGNATURE

                 After reasonable inquiry and to the best of my knowledge and
                 belief, I certify that the information set forth in this 
                 statement is true, complete and correct.




                 Date:     February 10, 1995                             
                                                                         
                                                                         
                 For:      Wachovia Corporation                          
                                                                         
                                                                         
                 By:                                                     
                           --------------------------------------------  
                           Hugh M. Durden, Executive Vice President 
              




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                 Certification:
                 ------------- 

                 By signing below, I certify that, to the best of my knowledge  
                 and belief, the securities referred to above were not acquired
                 for the purpose of and do not have the effect of changing or
                 influencing the control of the issuer of such securities and
                 were not acquired in connection with or as a participant in any
                 transaction having such purposes or effect.



                                         SIGNATURE

                 After reasonable inquiry and to the best of my knowledge and
                 belief, I certify that the information set forth in this
                 statement is true, complete and correct.




                 Date:     February 10, 1995                            
                                                                        
                                                                        
                 For:      Wachovia Bank of North Carolina, NA          
                                                                        
                                                                        
                 By:                                                    
                           -------------------------------------------- 
                           Dennis R. Monroe, Senior Vice President      
              




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