diff --git a/graphql/resolve/query_rewriter.go b/graphql/resolve/query_rewriter.go
index 20e6e511d2a..e5a69e8f9c1 100644
--- a/graphql/resolve/query_rewriter.go
+++ b/graphql/resolve/query_rewriter.go
@@ -651,9 +651,9 @@ func rewriteAsSimilarByIdQuery(
 	distanceFormula := "math(sqrt((v2 - v1) dot (v2 - v1)))" // default - euclidean
 
 	if metric == schema.SimilarSearchMetricDotProduct {
-		distanceFormula = "math((1.0 - (v1 dot v2)) /2.0)"
+		distanceFormula = "math(1.0 - (v1 dot v2))"
 	} else if metric == schema.SimilarSearchMetricCosine {
-		distanceFormula = "math((1.0 - ((v1 dot v2) / sqrt( (v1 dot v1) * (v2 dot v2) ) )) / 2.0)"
+		distanceFormula = "math(1.0 - ((v1 dot v2) / sqrt( (v1 dot v1) * (v2 dot v2) )))"
 	}
 
 	// First generate the query to fetch the uid
@@ -698,6 +698,32 @@ func rewriteAsSimilarByIdQuery(
 	//	  v2 as Product.embedding
 	//	  distance as math((v2 - v1) dot (v2 - v1))
 	//  }
+	similarToArgs := []dql.Arg{
+		{
+			Value: pred,
+		},
+		{
+			Value: fmt.Sprintf("%v", topK),
+		},
+		{
+			Value: "val(v1)",
+		},
+	}
+
+	// Add optional ef parameter if provided (using "ef: value" format)
+	if ef := query.ArgValue(schema.SimilarEfArgName); ef != nil {
+		similarToArgs = append(similarToArgs,
+			dql.Arg{Value: fmt.Sprintf("%s: %v", schema.SimilarEfArgName, ef)},
+		)
+	}
+
+	// Add optional distance_threshold parameter if provided (using "distance_threshold: value" format)
+	if dt := query.ArgValue(schema.SimilarDistanceThresholdArgName); dt != nil {
+		similarToArgs = append(similarToArgs,
+			dql.Arg{Value: fmt.Sprintf("%s: %v", schema.SimilarDistanceThresholdArgName, dt)},
+		)
+	}
+
 	similarQuery := &dql.GraphQuery{
 		Attr: "var",
 		Children: []*dql.GraphQuery{
@@ -712,17 +738,7 @@ func rewriteAsSimilarByIdQuery(
 		},
 		Func: &dql.Function{
 			Name: "similar_to",
-			Args: []dql.Arg{
-				{
-					Value: pred,
-				},
-				{
-					Value: fmt.Sprintf("%v", topK),
-				},
-				{
-					Value: "val(v1)",
-				},
-			},
+			Args: similarToArgs,
 		},
 	}
 
@@ -811,10 +827,10 @@ func rewriteAsSimilarByEmbeddingQuery(
 	distanceFormula := "math(sqrt((v2 - $search_vector) dot (v2 - $search_vector)))" // default = euclidean
 
 	if metric == schema.SimilarSearchMetricDotProduct {
-		distanceFormula = "math(( 1.0 - (($search_vector) dot v2)) /2.0)"
+		distanceFormula = "math(1.0 - (($search_vector) dot v2))"
 	} else if metric == schema.SimilarSearchMetricCosine {
-		distanceFormula = "math((1.0 - ( (($search_vector) dot v2) / sqrt( (($search_vector) dot ($search_vector))" +
-			" * (v2 dot v2) ) )) / 2.0)"
+		distanceFormula = "math(1.0 - ((($search_vector) dot v2) / sqrt( (($search_vector) dot ($search_vector))" +
+			" * (v2 dot v2) )))"
 	}
 
 	// Save vectorString as a query variable, $search_vector
@@ -834,19 +850,35 @@ func rewriteAsSimilarByEmbeddingQuery(
 	// Create similar_to as the root function, passing $search_vector as
 	// the search vector
 	dgQuery[0].Attr = "var"
+	similarToArgs := []dql.Arg{
+		{
+			Value: pred,
+		},
+		{
+			Value: fmt.Sprintf("%v", topK),
+		},
+		{
+			Value: "$search_vector",
+		},
+	}
+
+	// Add optional ef parameter if provided (using "ef: value" format)
+	if ef := query.ArgValue(schema.SimilarEfArgName); ef != nil {
+		similarToArgs = append(similarToArgs,
+			dql.Arg{Value: fmt.Sprintf("%s: %v", schema.SimilarEfArgName, ef)},
+		)
+	}
+
+	// Add optional distance_threshold parameter if provided (using "distance_threshold: value" format)
+	if dt := query.ArgValue(schema.SimilarDistanceThresholdArgName); dt != nil {
+		similarToArgs = append(similarToArgs,
+			dql.Arg{Value: fmt.Sprintf("%s: %v", schema.SimilarDistanceThresholdArgName, dt)},
+		)
+	}
+
 	dgQuery[0].Func = &dql.Function{
 		Name: "similar_to",
-		Args: []dql.Arg{
-			{
-				Value: pred,
-			},
-			{
-				Value: fmt.Sprintf("%v", topK),
-			},
-			{
-				Value: "$search_vector",
-			},
-		},
+		Args: similarToArgs,
 	}
 
 	// Compute the euclidean distance between the neighbor
diff --git a/graphql/resolve/query_test.yaml b/graphql/resolve/query_test.yaml
index a9bae8e59b8..3465384e575 100644
--- a/graphql/resolve/query_test.yaml
+++ b/graphql/resolve/query_test.yaml
@@ -3432,7 +3432,7 @@
       }
       var(func: similar_to(ProjectCosine.description_v, 3, val(v1))) {
         v2 as ProjectCosine.description_v
-        distance as math((1.0 - ((v1 dot v2) / sqrt( (v1 dot v1) * (v2 dot v2) ) )) / 2.0)
+        distance as math(1.0 - ((v1 dot v2) / sqrt( (v1 dot v1) * (v2 dot v2) )))
       }
       querySimilarProjectCosineById(func: uid(distance), orderasc: val(distance)) {
         ProjectCosine.id : ProjectCosine.id
@@ -3457,7 +3457,7 @@
     query querySimilarProjectCosineByEmbedding($search_vector:  float32vector = "[0.1,0.2,0.3,0.4,0.5]") {
       var(func: similar_to(ProjectCosine.description_v, 1, $search_vector)) @filter(type(ProjectCosine)) {
         v2 as ProjectCosine.description_v
-        distance as math((1.0 - ( (($search_vector) dot v2) / sqrt( (($search_vector) dot ($search_vector)) * (v2 dot v2) ) )) / 2.0)
+        distance as math(1.0 - ((($search_vector) dot v2) / sqrt( (($search_vector) dot ($search_vector)) * (v2 dot v2) )))
       }
       querySimilarProjectCosineByEmbedding(func: uid(distance), orderasc: val(distance)) {
         ProjectCosine.id : ProjectCosine.id
@@ -3487,7 +3487,7 @@
       }
       var(func: similar_to(ProjectDotProduct.description_v, 3, val(v1))) {
         v2 as ProjectDotProduct.description_v
-        distance as math((1.0 - (v1 dot v2)) /2.0)
+        distance as math(1.0 - (v1 dot v2))
       }
       querySimilarProjectDotProductById(func: uid(distance), orderasc: val(distance)) {
         ProjectDotProduct.id : ProjectDotProduct.id
@@ -3512,7 +3512,7 @@
     query querySimilarProjectDotProductByEmbedding($search_vector:  float32vector = "[0.1,0.2,0.3,0.4,0.5]") {
       var(func: similar_to(ProjectDotProduct.description_v, 1, $search_vector)) @filter(type(ProjectDotProduct)) {
         v2 as ProjectDotProduct.description_v
-        distance as math(( 1.0 - (($search_vector) dot v2)) /2.0)
+        distance as math(1.0 - (($search_vector) dot v2))
       }
       querySimilarProjectDotProductByEmbedding(func: uid(distance), orderasc: val(distance)) {
         ProjectDotProduct.id : ProjectDotProduct.id
@@ -3522,3 +3522,171 @@
         ProjectDotProduct.vector_distance : val(distance)
       }
     }
+
+- name: query similar_to with ef parameter
+  gqlquery: |
+    query {
+      querySimilarProductByEmbedding(by: productVector, topK: 5, vector: [0.1, 0.2, 0.3, 0.4, 0.5], ef: 64) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query querySimilarProductByEmbedding($search_vector:  float32vector = "[0.1,0.2,0.3,0.4,0.5]") {
+      var(func: similar_to(Product.productVector, 5, $search_vector, ef: 64)) @filter(type(Product)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - $search_vector) dot (v2 - $search_vector)))
+      }
+      querySimilarProductByEmbedding(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
+
+- name: query similar_to with distance_threshold parameter
+  gqlquery: |
+    query {
+      querySimilarProductByEmbedding(by: productVector, topK: 10, vector: [0.1, 0.2, 0.3, 0.4, 0.5], distance_threshold: 0.5) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query querySimilarProductByEmbedding($search_vector:  float32vector = "[0.1,0.2,0.3,0.4,0.5]") {
+      var(func: similar_to(Product.productVector, 10, $search_vector, distance_threshold: 0.5)) @filter(type(Product)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - $search_vector) dot (v2 - $search_vector)))
+      }
+      querySimilarProductByEmbedding(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
+
+- name: query similar_to with both ef and distance_threshold parameters
+  gqlquery: |
+    query {
+      querySimilarProductByEmbedding(by: productVector, topK: 8, vector: [0.1, 0.2, 0.3, 0.4, 0.5], ef: 128, distance_threshold: 0.75) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query querySimilarProductByEmbedding($search_vector:  float32vector = "[0.1,0.2,0.3,0.4,0.5]") {
+      var(func: similar_to(Product.productVector, 8, $search_vector, ef: 128, distance_threshold: 0.75)) @filter(type(Product)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - $search_vector) dot (v2 - $search_vector)))
+      }
+      querySimilarProductByEmbedding(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
+
+- name: query vector by id with ef parameter
+  gqlquery: |
+    query {
+      querySimilarProductById(by: productVector, topK: 5, id: "0x1", ef: 64) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query {
+      var(func: eq(Product.id, "0x1")) @filter(type(Product)) {
+        vec as Product.productVector
+      }
+      var() {
+        v1 as max(val(vec))
+      }
+      var(func: similar_to(Product.productVector, 5, val(v1), ef: 64)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - v1) dot (v2 - v1)))
+      }
+      querySimilarProductById(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
+
+- name: query vector by id with distance_threshold parameter
+  gqlquery: |
+    query {
+      querySimilarProductById(by: productVector, topK: 10, id: "0x1", distance_threshold: 0.5) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query {
+      var(func: eq(Product.id, "0x1")) @filter(type(Product)) {
+        vec as Product.productVector
+      }
+      var() {
+        v1 as max(val(vec))
+      }
+      var(func: similar_to(Product.productVector, 10, val(v1), distance_threshold: 0.5)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - v1) dot (v2 - v1)))
+      }
+      querySimilarProductById(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
+
+- name: query vector by id with both ef and distance_threshold parameters
+  gqlquery: |
+    query {
+      querySimilarProductById(by: productVector, topK: 8, id: "0x1", ef: 128, distance_threshold: 0.75) {
+        id
+        title
+        productVector
+      }
+    }
+
+  dgquery: |-
+    query {
+      var(func: eq(Product.id, "0x1")) @filter(type(Product)) {
+        vec as Product.productVector
+      }
+      var() {
+        v1 as max(val(vec))
+      }
+      var(func: similar_to(Product.productVector, 8, val(v1), ef: 128, distance_threshold: 0.75)) {
+        v2 as Product.productVector
+        distance as math(sqrt((v2 - v1) dot (v2 - v1)))
+      }
+      querySimilarProductById(func: uid(distance), orderasc: val(distance)) {
+        Product.id : Product.id
+        Product.title : Product.title
+        Product.productVector : Product.productVector
+        dgraph.uid : uid
+        Product.vector_distance : val(distance)
+      }
+    }
diff --git a/graphql/schema/gqlschema.go b/graphql/schema/gqlschema.go
index ae4cf684295..32eda06f88f 100644
--- a/graphql/schema/gqlschema.go
+++ b/graphql/schema/gqlschema.go
@@ -2088,6 +2088,25 @@ func addSimilarByEmbeddingQuery(schema *ast.Schema, defn *ast.Definition) {
 			NonNull: true,
 		},
 	})
+
+	// Accept optional ef parameter for HNSW search
+	qry.Arguments = append(qry.Arguments, &ast.ArgumentDefinition{
+		Name: SimilarEfArgName,
+		Type: &ast.Type{
+			NamedType: "Int",
+			NonNull:   false,
+		},
+	})
+
+	// Accept optional distance_threshold parameter for filtering results
+	qry.Arguments = append(qry.Arguments, &ast.ArgumentDefinition{
+		Name: SimilarDistanceThresholdArgName,
+		Type: &ast.Type{
+			NamedType: "Float",
+			NonNull:   false,
+		},
+	})
+
 	addFilterArgument(schema, qry)
 
 	schema.Query.Fields = append(schema.Query.Fields, qry)
@@ -2197,6 +2216,24 @@ func addSimilarByIdQuery(schema *ast.Schema, defn *ast.Definition,
 		},
 	})
 
+	// Accept optional ef parameter for HNSW search
+	qry.Arguments = append(qry.Arguments, &ast.ArgumentDefinition{
+		Name: SimilarEfArgName,
+		Type: &ast.Type{
+			NamedType: "Int",
+			NonNull:   false,
+		},
+	})
+
+	// Accept optional distance_threshold parameter for filtering results
+	qry.Arguments = append(qry.Arguments, &ast.ArgumentDefinition{
+		Name: SimilarDistanceThresholdArgName,
+		Type: &ast.Type{
+			NamedType: "Float",
+			NonNull:   false,
+		},
+	})
+
 	addFilterArgument(schema, qry)
 	schema.Query.Fields = append(schema.Query.Fields, qry)
 }
diff --git a/graphql/schema/testdata/schemagen/output/embedding-directive-with-similar-queries.graphql b/graphql/schema/testdata/schemagen/output/embedding-directive-with-similar-queries.graphql
index f7b1699c512..351d2eb769b 100644
--- a/graphql/schema/testdata/schemagen/output/embedding-directive-with-similar-queries.graphql
+++ b/graphql/schema/testdata/schemagen/output/embedding-directive-with-similar-queries.graphql
@@ -553,15 +553,15 @@ input UserRef {
 
 type Query {
 	getProduct(id: String!): Product
-	querySimilarProductById(id: String!, by: ProductEmbedding!, topK: Int!, filter: ProductFilter): [Product]
-	querySimilarProductByEmbedding(by: ProductEmbedding!, topK: Int!, vector: [Float!]!, filter: ProductFilter): [Product]
+	querySimilarProductById(id: String!, by: ProductEmbedding!, topK: Int!, ef: Int, distance_threshold: Float, filter: ProductFilter): [Product]
+	querySimilarProductByEmbedding(by: ProductEmbedding!, topK: Int!, vector: [Float!]!, ef: Int, distance_threshold: Float, filter: ProductFilter): [Product]
 	queryProduct(filter: ProductFilter, order: ProductOrder, first: Int, offset: Int): [Product]
 	aggregateProduct(filter: ProductFilter): ProductAggregateResult
 	queryPurchase(filter: PurchaseFilter, order: PurchaseOrder, first: Int, offset: Int): [Purchase]
 	aggregatePurchase(filter: PurchaseFilter): PurchaseAggregateResult
 	getUser(email: String!): User
-	querySimilarUserById(email: String!, by: UserEmbedding!, topK: Int!, filter: UserFilter): [User]
-	querySimilarUserByEmbedding(by: UserEmbedding!, topK: Int!, vector: [Float!]!, filter: UserFilter): [User]
+	querySimilarUserById(email: String!, by: UserEmbedding!, topK: Int!, ef: Int, distance_threshold: Float, filter: UserFilter): [User]
+	querySimilarUserByEmbedding(by: UserEmbedding!, topK: Int!, vector: [Float!]!, ef: Int, distance_threshold: Float, filter: UserFilter): [User]
 	queryUser(filter: UserFilter, order: UserOrder, first: Int, offset: Int): [User]
 	aggregateUser(filter: UserFilter): UserAggregateResult
 }
diff --git a/graphql/schema/wrappers.go b/graphql/schema/wrappers.go
index 8837d5170d8..f30df66a50d 100644
--- a/graphql/schema/wrappers.go
+++ b/graphql/schema/wrappers.go
@@ -76,38 +76,40 @@ type EntityRepresentations struct {
 
 // Query/Mutation types and arg names
 const (
-	GetQuery                      QueryType    = "get"
-	SimilarByIdQuery              QueryType    = "querySimilarById"
-	SimilarByEmbeddingQuery       QueryType    = "querySimilarByEmbedding"
-	FilterQuery                   QueryType    = "query"
-	AggregateQuery                QueryType    = "aggregate"
-	SchemaQuery                   QueryType    = "schema"
-	EntitiesQuery                 QueryType    = "entities"
-	PasswordQuery                 QueryType    = "checkPassword"
-	HTTPQuery                     QueryType    = "http"
-	DQLQuery                      QueryType    = "dql"
-	NotSupportedQuery             QueryType    = "notsupported"
-	AddMutation                   MutationType = "add"
-	UpdateMutation                MutationType = "update"
-	DeleteMutation                MutationType = "delete"
-	HTTPMutation                  MutationType = "http"
-	NotSupportedMutation          MutationType = "notsupported"
-	IDType                                     = "ID"
-	InputArgName                               = "input"
-	UpsertArgName                              = "upsert"
-	FilterArgName                              = "filter"
-	SimilarByArgName                           = "by"
-	SimilarTopKArgName                         = "topK"
-	SimilarVectorArgName                       = "vector"
-	EmbeddingEnumSuffix                        = "Embedding"
-	SimilarQueryPrefix                         = "querySimilar"
-	SimilarByIdQuerySuffix                     = "ById"
-	SimilarByEmbeddingQuerySuffix              = "ByEmbedding"
-	SimilarQueryResultTypeSuffix               = "WithDistance"
-	SimilarQueryDistanceFieldName              = "vector_distance"
-	SimilarSearchMetricEuclidean               = "euclidean"
-	SimilarSearchMetricDotProduct              = "dotproduct"
-	SimilarSearchMetricCosine                  = "cosine"
+	GetQuery                        QueryType    = "get"
+	SimilarByIdQuery                QueryType    = "querySimilarById"
+	SimilarByEmbeddingQuery         QueryType    = "querySimilarByEmbedding"
+	FilterQuery                     QueryType    = "query"
+	AggregateQuery                  QueryType    = "aggregate"
+	SchemaQuery                     QueryType    = "schema"
+	EntitiesQuery                   QueryType    = "entities"
+	PasswordQuery                   QueryType    = "checkPassword"
+	HTTPQuery                       QueryType    = "http"
+	DQLQuery                        QueryType    = "dql"
+	NotSupportedQuery               QueryType    = "notsupported"
+	AddMutation                     MutationType = "add"
+	UpdateMutation                  MutationType = "update"
+	DeleteMutation                  MutationType = "delete"
+	HTTPMutation                    MutationType = "http"
+	NotSupportedMutation            MutationType = "notsupported"
+	IDType                                       = "ID"
+	InputArgName                                 = "input"
+	UpsertArgName                                = "upsert"
+	FilterArgName                                = "filter"
+	SimilarByArgName                             = "by"
+	SimilarTopKArgName                           = "topK"
+	SimilarVectorArgName                         = "vector"
+	SimilarEfArgName                             = "ef"
+	SimilarDistanceThresholdArgName              = "distance_threshold"
+	EmbeddingEnumSuffix                          = "Embedding"
+	SimilarQueryPrefix                           = "querySimilar"
+	SimilarByIdQuerySuffix                       = "ById"
+	SimilarByEmbeddingQuerySuffix                = "ByEmbedding"
+	SimilarQueryResultTypeSuffix                 = "WithDistance"
+	SimilarQueryDistanceFieldName                = "vector_distance"
+	SimilarSearchMetricEuclidean                 = "euclidean"
+	SimilarSearchMetricDotProduct                = "dotproduct"
+	SimilarSearchMetricCosine                    = "cosine"
 )
 
 // Schema represents a valid GraphQL schema
@@ -1388,7 +1390,9 @@ func (f *field) IDArgValue() (xids map[string]string, uid uint64, err error) {
 		if (idField == nil || arg.Name != idField.Name()) &&
 			(passwordField == nil || arg.Name != passwordField.Name()) &&
 			(queryType(f.field.Name, nil) != SimilarByIdQuery ||
-				(arg.Name != SimilarTopKArgName && arg.Name != SimilarByArgName && arg.Name != "filter")) {
+				(arg.Name != SimilarTopKArgName && arg.Name != SimilarByArgName &&
+					arg.Name != SimilarEfArgName && arg.Name != SimilarDistanceThresholdArgName &&
+					arg.Name != "filter")) {
 			xidArgName = arg.Name
 		}