diff --git a/mmv1/templates/terraform/constants/disk.erb b/mmv1/templates/terraform/constants/disk.erb
index d170c7cb4195..7986ddce1fa1 100644
--- a/mmv1/templates/terraform/constants/disk.erb
+++ b/mmv1/templates/terraform/constants/disk.erb
@@ -120,6 +120,10 @@ func diskImageFamilyEquals(imageName, familyName string) bool {
 		return true
 	}
 
+	if suppressCosFamilyDiff(imageName, familyName) {
+		return true
+	}
+
 	if suppressWindowsSqlFamilyDiff(imageName, familyName) {
 		return true
 	}
@@ -144,6 +148,19 @@ func suppressCanonicalFamilyDiff(imageName, familyName string) bool {
 	return false
 }
 
+// e.g. image: cos-NN-*, family: cos-NN-lts
+func suppressCosFamilyDiff(imageName, familyName string) bool {
+	parts := cosLtsImage.FindStringSubmatch(imageName)
+	if len(parts) == 2 {
+		f := fmt.Sprintf("cos-%s-lts", parts[1])
+		if f == familyName {
+			return true
+		}
+	}
+
+	return false
+}
+
 // e.g. image: sql-2017-standard-windows-2016-dc-v20180109, family: sql-std-2017-win-2016
 // e.g. image: sql-2017-express-windows-2012-r2-dc-v20180109, family: sql-exp-2017-win-2012-r2
 func suppressWindowsSqlFamilyDiff(imageName, familyName string) bool {
diff --git a/mmv1/third_party/terraform/tests/resource_compute_disk_test.go.erb b/mmv1/third_party/terraform/tests/resource_compute_disk_test.go.erb
index e7ce12c1bba6..d313a9b13d45 100644
--- a/mmv1/third_party/terraform/tests/resource_compute_disk_test.go.erb
+++ b/mmv1/third_party/terraform/tests/resource_compute_disk_test.go.erb
@@ -127,6 +127,11 @@ func TestDiskImageDiffSuppress(t *testing.T) {
 			New:                "ubuntu-minimal-1804-lts",
 			ExpectDiffSuppress: true,
 		},
+		"matching unconventional image family - cos": {
+			Old:                "https://www.googleapis.com/compute/v1/projects/cos-cloud/global/images/cos-85-13310-1209-17",
+			New:                "cos-85-lts",
+			ExpectDiffSuppress: true,
+		},
 		"different image family": {
 			Old:                "https://www.googleapis.com/compute/v1/projects/debian-cloud/global/images/debian-8-jessie-v20171213",
 			New:                "family/debian-7",
diff --git a/mmv1/third_party/terraform/utils/image.go b/mmv1/third_party/terraform/utils/image.go
index 61ac117dc9e7..ad90c55cef83 100644
--- a/mmv1/third_party/terraform/utils/image.go
+++ b/mmv1/third_party/terraform/utils/image.go
@@ -27,6 +27,7 @@ var (
 
 	windowsSqlImage         = regexp.MustCompile("^sql-(?:server-)?([0-9]{4})-([a-z]+)-windows-(?:server-)?([0-9]{4})(?:-r([0-9]+))?-dc-v[0-9]+$")
 	canonicalUbuntuLtsImage = regexp.MustCompile("^ubuntu-(minimal-)?([0-9]+)-")
+	cosLtsImage             = regexp.MustCompile("^cos-([0-9]+)-")
 )
 
 // built-in projects to look for images/families containing the string